ULTRAFAST ELECTRON CRYSTALLOGRAPHY STUDIES OF CHARGE-DENSITY WAVES MATERIALS AND NANOSCALE ICE By Tzong-Ru Terry Han A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of Physics - Doctor of Philosophy 2015 ABSTRACT ULTRAFAST ELECTRON CRYSTALLOGRAPHY STUDIES OF CHARGE-DENSITY WAVES MATERALS AND NANOSCALE ICE By Tzong-Ru Terry Han The main focus of this dissertation is centered around the study of structural dynamics and phase transition in charge-density wave (CDW) materials. Due to their quasi-reduced dimensionality, a CDW presents a unique system to study the interplay between electron and lattice, effect of symmetry breaking, and electronic condensates. Femtosecond time-resolved pump-probe technique with electron crystallography offers the perfect tool to disentangle the two main players in CDW: electrons and ions. By illumination with intense femtosecond optical pulses to increase the electron energy, we monitor how the energy flows to other subsystems, and explore regions of the energy landscape that are not accessible through conventional methods. Taking advantages of the uniaxial CDW formation of CeTe3 that allows us to differentiate nonCDW-related contributions to the lattice response, we isolate the CDW-related structural response from the thermal effects on lattice. From the two-component structural dynamics, we examine how strongly the electron and lattice couple to each other, and further distinguish the internal energy transfer between each charge and lattice subsystems. From this CeTe3 experiment, we provide an explanation to a signature phenomenon belonging to "classical Peierls" CDW systems. Compared to the classical CDW in CeTe3, 1T-TaS2 is at the other end of spectrum with its well decorated phase diagram including almost all flavors of CDW, Mott insulating, and superconducting states. Utilizing femtosecond photo-doping, we explore the energy landscape for states or phases that are not accessible by other conventional means, like chemical doping and pressure induced modification. The remaining part of this dissertation presents the journey we embarked on when trying to unveil the mystery of water, the ubiquitous molecule that sustains life on earth. Utilizing water delivery system designed specifically for our ultra-high-vacuum chamber, we explore the structural change near the water phase boundary and carrier redistribution or diffusion at the water/nanoparticle/silicon interface. To my family iv ACKNOWLEDGMENTS First and foremost, I would like to thank my advisor Prof. Chong-Yu Ruan for his patience, support, advice, and guidance. I came to MSU wishing to learn "how to do science" but earned more than that. He taught me how to manage every project in life with planning, perspective, and the desire to overachieve. Next, I would like to thank my comrades, Zhensheng Tao and Kiseok Chang. Either in the lab or outside school, they helped me solve the problems I countered, shared the up-and-down moments and emotions with me, and carried me on their shoulder along the way. I also want to thank Faran Zhou for his help and company on many projects, especially when I was not available in the lab. I acknowledge my colleagues and collaborators for their advice and support throughout my time at MSU. Thank to Dr. Christos D. Malliakas and Prof. Kanatzidis at Northwestern University for their high-quality samples and scientific support for the CDW projects reported in this dissertation. Thanks to Prof. John McGuire for his guidance in the nonlinear optics setup for our water experiment. Thanks to Prof. William Pratt for his guidance when I T.A.ed his class in 2008. Thanks to Fei Yuan for his theoretical computation and helping hands in the lab. Thanks to two excellent MSU undergraduate students, Peter Lee and Thiago Szymanski, for their support and assistance in almost every project described in my dissertation. Thanks to every REU student I worked with who helped us advance many projects during the summer. Dr. Reza Loloee helped me greatly with his knowledge of many instruments and facilities that were crucial to my projects. Dr. Xudong Fan at the Center for Advanced Microscopy helped me on many problems I encountered with sample preparation and characterization. Dr. Baokang Bi trained and advised me to utilize the equipments in the cleanroom and pushed the results I could obtain to the limit with those state-of-the-art instruments. To the machine shop staff Tom Palazzolo, Tom Hudson, Jum Muss, and Rob Bennett for their impeccable skills in producing precise instruments for my projects and v their patience on teaching me how to keep all my fingers when I was working in the student machine shop. Big thanks are also due to Cathy Cords, Debbie Barratt, and Kim Crosslan for their fantastic administrative support. In all, I would like to thank everyone in the physics department at MSU for their friendly smiles and nurturing conversations. The MSU family is warmer than the freezing Michigan weather. On the personal side, I would like to thank the unconditional love from my parents. Last but not least, I want to thank my wife Peggy Wu. She gave me the freedom to pursue my career goal and the courage to keep going when I wanted to give up. I came to MSU seeking knowledge and advice, but I earned life-changing experience, life-long friendship, and unforgettable memories. vi TABLE OF CONTENTS LIST OF TABLES......................................................................................................................................ix LIST OF FIGURES...................................................................................................................................x CHAPTER 1..................................................................................................................................................1 Strongly Correlated Complex Materials........................................................................................................1 1.1 Colossal Magnetoresistance Magnanites............................................................................2 1.2 Cuprate Superconductor.......................................................................................................6 1.3 Experimental Challenges.....................................................................................................9 CHAPTER 2................................................................................................................................................10 Charge-Density Waves Materials................................................................................................................10 2.1 Overview on Charge-Density Waves.................................................................................11 2.1.1 Nearly Free Electron in One Dimensional Conduction Band...............................11 2.1.2 The Lindhard Response Function of Electron Gas...............................................13 2.1.3 Instabilities in a One-Dimensional Electron Gas..................................................18 2.1.4 The Kohn Anomaly and the Peierls Transition....................................................20 2.1.5 Collective Excitation of Charge-Density Waves..................................................27 2.2 Charge-Density Waves Investigated by Various Techniques and Scientific Outstanding Questions............................................................................................................................29 CHAPTER 3................................................................................................................................................32 Ultrafast Electron Crystallography Techniques for Studying Low Dimensional Material CeTe3...............32 3.1 Diffraction Theory.............................................................................................................33 3.1.1 Diffraction Condition............................................................................................33 3.1.2 Scattered Intensity.................................................................................................35 3.1.3 The Debye Waller Effect......................................................................................39 3.2 CeTe3 Sample Preparation and Characterization...............................................................42 3.3 Experimental Setup............................................................................................................47 CHAPTER 4................................................................................................................................................50 Structural Dynamics of Charge-Density Waves..........................................................................................50 4.1 Background on CeTe3........................................................................................................51 4.2 Experiments on CeTe3.......................................................................................................55 4.2.1 CeTe3 Experimental Setup and Methods..............................................................55 4.2.2 Asymmetric Characters of CeTe3.........................................................................57 4.2.3 Dynamics of Order Parameter of CDW in CeTe3.................................................59 4.2.4 Cooperativity Between Electronic and Structural Subsystems.............................62 4.2.5 Summary...............................................................................................................65 CHAPTER 5................................................................................................................................................67 Phase Transition of Charge-Density Waves................................................................................................67 5.1 Crystal Structure and Charge-Density Waves of 1T-TaS2................................................68 5.2 Exploration of Meta-Stability and Hidden Phases of 1T-TaS2.........................................71 5.3 Additional Materials for 1T-TaS2 experiment...................................................................85 5.3.1 Sample Preparation...............................................................................................85 5.3.2 Experimental Details.............................................................................................87 5.3.3 Data Analysis for 1T-TaS2 Experiment...............................................................88 vii 5.3.4 5.3.5 Calculation of Energy and Photon Density..........................................................89 Constructing Phase Diagram................................................................................91 CHAPTER 6................................................................................................................................................92 Dynamics of Nanoscale Water on Surface..................................................................................................92 6.1 Structure and Dynamics of Water......................................................................................93 6.2 Experiment Setup...............................................................................................................97 6.3 Generation of Mid-IR Excitation Laser via Nonlinear Optics.........................................100 6.4 Ice/Water Deposition on Substrate Using Molecular Beam Doser.................................107 6.5 Ice/Water Experiment Result...........................................................................................112 CHAPTER 7..............................................................................................................................................115 Surface-Plasmonic-Resonance Enhanced Interfacial Charge Transfer.....................................................115 7.1 Introduction......................................................................................................................116 7.2 Ultrafast Diffractive Photovoltammetry Methodology and Experiment Setup...............118 7.3 Charge Transfer between Nanoparticles and Substrate Enhanced by Surface Plasmon Resonance Excitation with the Coverage of Water-Ice...................................................120 CHAPTER 8..............................................................................................................................................125 Summary....................................................................................................................................................125 APPENDICES...........................................................................................................................................127 Appendix A Electron Counting and Statistical Uncertainties.................................................128 Appendix B Two Component Fitting and Statistical Analysis...............................................130 Appendix C Carbon Nanotube Sample Preparation................................................................133 Appendix D Tsunami Alignment............................................................................................135 Appendix E Optimization at Spitfire for Optimal Output of Mid-IR Laser...........................138 Appendix F Gold Nano-Particle Deposition on ITO..............................................................139 BIBLIGRAPHY………………………………………………………………………………………….140 viii LIST OF TABLES Table 2.1.1 Various broken-symmetry ground states of one-dimensional metals [Dre 2002]……….19 Table 5.1.1 The different CDW phase in 1T-TaS2 and their manifestation in reciprocal space. The values of transition temperature and angle associated with different CDW phases under the thermodynamic conditions (cooling and warming) are taken from [Spi 1997] [Ish 1991]..................................................................................................................…...70 ix LIST OF FIGURES Figure 1.1.1 Previous studies on CMR. (a) Magnetoresistance measurement at room temperature for La-Ba-Mn-O thin films. (b) Temperature dependence of resistivity (R), resistivity (), and magnetization (M) of La-Ca-Mn-O films.....................................................................3 Figure 1.1.2 Previous studies on CMR. (a) Induced change in transmitted electric field. (b) Induced change in real conductivity..................................................................................................4 Figure 1.1.3 Previous studies on CMR. (a) Contribution of spin and phonon to conductivity at different temperature (b) Phase diagram of La1-xCaxMnO3 showing phases including charge-ordering (CO), antiferromagnet (AF), canted antiferromagnet (CAF), ferromagnetic (FM), and ferromagnetic insulator (FI). (c) Linescan of TEM images in the a (red line) and c (blue line) showing the satellite peaks only present in the a direction. (d) and (e) Differential resistivity versus d.c. bias applied in the a (red lines) and c (blue lines) directions at various temperatures..............................................................................5 Figure 1.2.1 Previous studies on Cuprates. (a) Diffraction intensity crossing a common point at different delay time at different fluence. (b) Threshold in fluence that would initiate the phase transition. (c) Typical photoemission data at Fermi surface showing change in electron dispersion and spectra after optical excitation. (d) Dynamics of superconducting gap magnitude at two locations.........................................................................................7 Figure 2.1.1 Band structure of two electron models. (a) Energy versus wavevector for a free electron (b) Energy versus wavevector, or band structure, for an electron in a monatomic linear lattice of lattice constant [Kit 2004].....................................................................12 Figure 2.1.2 Responses with different dimensions. (a) The Lindhard response function for different dimensions. (b) and (c) The Fermi surface, noted in red lines, and Fermi nesting, the condition with a common paring wavevector at Fermi surface. (d) The pairs of one full and one empty states can be connected by the wavevector ................................15 Figure 2.1.3 Low-dimension gas. (a) Fermi surface of a quasi-one-dimensional electron gas [Grü 1994]. (b) The response function of one-dimensional electron gas at various temperatures [Hee 1979].........................................................................................................................17 Figure 2.1.4 The Kohn anomaly. (a) The Kohn anomaly of acoustic phonon frequency showing Kohn anomaly at temperature above the mean field transition temperature. (b) Phonon dispersion relationship of 1D, 2D, and 3D dimensional metals [Grü 1994].......22 Figure 2.1.5 The single particle band, electron density, and lattice distortion in (a) state above and (b) in CDW state at . (c) The temperature dependence of band gap and the renormalized phonon frequency . Both carries a characteristic dependence of .....................................................................................................................25 Figure 2.1.6 CDW states. (a) CDW ground state (b) Phase mode (c) Amplitude mode. The dotted lines represents the electronic part of charge-density wave while the arrow indicates the displacement of ion core, as red dots, from the equilibrium position...............................27 x Figure 2.2.1 Previous studies on 1T-TaS2. (a) The time evolution of normalized reflectivity measured at different sample temperature, T = 45 and 110 K displayed in log scale to highlight the two time scale in relaxation [Dem 1999]. (b) the temperature dependence of relaxation time of 1T-TaS2, plotted with result taken upon warming in open symbols and cooling in solid symbols [Dem 2002]. (c) Dynamics of Hubbard peak normalized intensity of 1TTaS2 in Mott-insulator state [Per 2006]. (d) Shift of the Hubbard peak that recovers in ps time scale [Per 2006].........................................................................................................30 Figure 3.1.1 Diffraction. (a) Elastic scattering from two planes consisting identical atoms. Vectors ki and kf are the incident and scattered wave vectors. (b) Momentum transfer, s, being the vectorial change of incident and scattered wave vector, while θsc is the angle between incident and scattered wave vectors.....................................................34 Figure 3.1.2 Scattering process. (a) Generic schematic layout and notation of scattering process. (b) An electromagnetic plan wave polarized with its electric field along the z axis forces an electric dipole at the origin to oscillate [AN 2001]............................................................36 Figure 3.1.3 X-ray scattering event from (a) an atom, (b) a molecule, and (c) and a crystal [AN 2001]........................................................................................................................ .37 Figure 3.2.1 Equipments for sample preparation. (a) CeTe3 sample glued to the copper grid. (b) Custom grinder for thinning the sample. (c) Gatan 691 Ion Milling Machine.................43 Figure 3.2.2 TEM observation on CeTe3. (a) Ion-milled opening at CeTe3 sample. (b) CeTe3 film at the edge of the opening. The central dark spot is a burn mark on the CCD camera. (c) TEM diffraction image of CeTe3. The satellite peaks appear on the two sides of the Bragg reflection along c* direction (circled in red), while the main Bragg peaks, circled in blue, show square-symmetry along both a* and c* axes. (d) EDS element analysis of CeTe3 sample showing ~1:3 ratio of Ce:Te. The Carbon trace was contributed to the diamond lapping film used in the initial thinning of sample. The Copper trace was originated from the cooper TEM grid the CeTe3 was glued on.........................................44 Figure 3.2.3 Thickness map on CeTe3. (a) TEM picture taken without energy filter. (b) TEM picture taken with energy filter that blocks out energy-lost electrons. (c) Thickness map processed using (a) and (b). The scale bar in (c) also applies to (a) and (b). (d) Typical EELS from CeTe3 material. (e) Thickness profile of ion-milled CeTe3. ........................45 Figure 3.3.1 Experiment setup. (a) Layout of ultrafast electron crystallography apparatus. (b) Schematic diagram of the proximity-coupled femtosecond electron gun.........................48 Figure 3.3.2 Experiment setup. (a)The electron pulse-length as a function of the number of electrons per pulse employed. (b) Diffraction pattern of CeTe3 obtained from UEC setup.............49 Figure 4.1.1 Parameters of RETe3 family. (a) Energy density at Femi level as a function of the lattice parameter of RETe3. (b) CDW gap size in various RETe3 material [Bro 2008]. (c) CDW phase transition temperature in RETe3 where heavier RE element exhibit two CDW transition temperatures [Ru 2008].....................................................................................52 Figure 4.1.2 Parameters of CeTe3. (a) Crystal structure of CeTe3 with the corresponding reciprocal lattice. The lattice constant 4. 4 2 .0 and 4.40 (b) The real-space model of corrugated CeTe slab (gray/red) and Te net (red) viewed along the b-axis. The xi coupling from px and py orbital chains from Te is also included. (c) An almost square Fermi surface calculated from a tight-binding model with extended or reduced Brillouin zone, as well as two sets of 1D bands from coupling of px and py chains........................53 Figure 4.1.3 Fermi surface of CeTe3. (a) Fermi surface of CeTe3, calculated from a tight-binding model, consists the coupling from px (red), py (blue), and the limits of extended or reduced Brillouin zones [Ru 2008]. (b) Fermi surface of CeTe3 measured from APRES (solid black line) [Bro 2004]..............................................................................................54 Figure 4.2.1 Experiment result on CeTe3. (a) Crystal structure of CeTe3 with the corresponding reciprocal lattice assignment with a=4.384Å, b=26.05Å, and c=4.403Å [Mal 2005]. Our femtosecond (fs) electron pulse is directed along the b-axis, producing a transmission diffraction pattern, while the fs laser pulses excite the sample area at 45o angle. (b) The top panel shows the 3D diffraction intensity map, where the CDW satellites are located at a*± Q0 in the dashed region. The lower panels display the temporal evolution of ultrafast electron crystallography patterns subtracted by the equilibrium state pattern taken before fs laser excitation (t < 0) to showcase the induced changes. The panels show both the ps sequences for Bragg reflections and fs-to-ps sequences in a scaled-up view of the region near CDW satellites.....................................................................................56 Figure 4.2.2 Dynamics of CeTe3. (a) The normalized Bragg peak intensity at q=-4a* and 4c* under three different laser fluences: F=2.42, 4.62, and 7.30 mJ/cm2. The error bars are based on electron counting statistics. (see Appendix A). (b) The normalized satellite intensity at qcdw=3a*+Q0 shows a nonscalable two-step suppression..............................................58 Figure 4.2.3 Dynamics of CeTe3. (a) Detailed view of satellite intensity change at early times showing a two-step suppression, along with the two-component fits. The data from F=2.43 mJ/cm2 are multiplied by 3 in order to compare with data from F=7.30 mJ/cm2. The dashed curve shows the fitted result for F=7.30 mJ/cm2 data. The error bars are calculated based on the counting statistics. (b) The fast component of the satellite suppression , showing a fast decay and recovery. The inset shows the amplitude of the fast and slow components extracted from fitting..................................59 Figure 4.1.4 Order parameter of CeTe3 CDW. (a) the temporal evolution of the structural order parameter . The reduction of represents symmetry recovery as described by the CDW potential evolving from double well to single well (insert). (b) The CDW collective mode fluctuational variance , deduced from anisotropy analysis. (c) CDW fluctuation amplitude order parameter correlation plot.........................................61 Figure 4.2.5 Conceptual framework of the three-temperature model (TTM). See text for notation....64 Figure 5.1.1 Structure of 1T-TaS2. (a) The tantalum atom is located at center of six octahedrally coordinated sulphur atoms. The lattice constant are 3.3649 Å and 5.8971 Å. [Spi 1997]. (b) The Star-of-David 13-atom cluster representing the unit cell of C-CDW in real space. The lattice distortion within each star is coupled with a strong charge density redistribution. The angle between the CDW vector and lattice vector is 13.9o...........................................................................................................................69 Figure 5.2.1 Phase diagram and diffraction pattern of 1T-TaS2. (a) Generic phase diagram of 1T-TaS2 under various physical domains (temperature, doping x, or pressure P ) reconstructed xii based on reference [Fau 2011] [Cav 2004] [Per 2006] The CDW phase evolution can be characterized by the changes in the hexagonal CDW diffraction peaks at reciprocal vector Q: Amongst the phase transitions starting from the C-CDW, the intensity of CDW and the angle of Q (with respect to G) are reduced suddenly at the phase boundaries to approximately half and 0 (from 13.9) to the IC-CDW (upper-right corner). (b) The scale-up view of the ultrafast electron diffraction pattern, showing the hexagonal diffraction patterns of C-CDW (Q) surrounding the lattice Bragg peaks (G)...................72 Figure 5.2.2 Transitions of 1T-TaS2 upon heating, showing complementary changes in the resistivity 1991].........................................................................................................75 Figure 5.2.3 Typical dynamics of Bragg and satellite (CDW) peaks of 1T-TaS2. Dynamics of each components have been normalized and scaled for comparison.........................................76 Figure 5.2.4. Comparison between the thermal and optically induced changes of over absorbed energy density (see section 5.3.4 for calculation). The temperature of 1T-TaS2 is at 150K initially............................................................................................................77 Figure 5.2.5 The optically induced evolution of CDW states characterized by CDW suppression (in ratio, based on unperturbed CDW intensity) and orientation angle at various absorbed photon density for two different pumps: 800 and 2500 nm..............................................78 Figure 5.2.6 The temperature – photon-density phase diagram of 1T-TaS2.........................................80 Figure 5.2.7 The dynamics of CDW state transformations inspected via the rotation of CDW wave vector Q away from C-CDW and the suppression of ICDW(t) [in ratio based on the ICDW(10 ps)]. The solid lines are drawn based on fitting the stair-case rises using a Gauss Error function...............................................................................................................81 Figure 5.2.8 Cartoon depiction of the dynamical evolution CDW states in a zig-zag pathway over the free energy contour defined by the changes in and A2 based on the dynamics extracted from (A). A is scaled to 0.15Å at C-CDW state based on reference [Spi 1997]...............83 Figure 5.3.1 Optical images of 1T-TaS2. (a) Optical picture of cleaved 1T-TaS2 from bulk as a starting piece for exfoliating. (b) 1T-TaS2 on scotch tape after exfoliated once. (c) Optical image of peeled 1T-TaS2 sample taken with light coming from below the sample stage. (d) 1T-TaS2 samples after multiple "peeling"........................................................86 Figure 5.3.2 Optical images of 1T-TaS2 samples. (a) Thin 1T-TaS2 samples on silicon surface. (b) 1T-TaS2 samples on TEM grid ready for UEC experiment...............................................87 Figure 5.3.3 Diffraction pattern of 1T-TaS2. (a) Diffraction pattern of 1T-TaS2 in the NC-CDW state taken at room temperature. The image is in logarithmic scale to make CDW peaks more visible. (b) Scale-up view of the diffraction pattern from the square region in (a), showing clear hexagonally distributed first-order CDW satellite peaks around the central lattice Bragg peaks. Second-order CDW satellite peaks are also visible. (c-e) Time-dependent diffraction images from a single Bragg peak region at different time delays: -1ps, +1ps, +3ps respectively. The solid line connects neighboring Bragg peaks, representing the direction of the lattice vector G. The dashed line connects neighboring CDW peaks, representing the direction of the CDW vector Q. ϕ represents the angle between CDW xiii and Bragg vectors. In (e), CDW vector rotates fully into the lattice vector direction, indicating that the NC-CDW is transformed to IC-CDW by 3 ps....................................89 Figure 5.3.4 The determination of CDW phase boundaries based on presence of a step or a slope change................................................................................................................................90 Figure 6.1.1 Purposed structure of water (a) LDL and (b) HDL [Cha 1999]..................................94 Figure 6.1.2 Optical studies on water (a) comparison of g(r) of liquid water measured at 7, 25, and 66oC with X-ray. (b) Raman spectra with 3115 cm-1 pumping, fit using the two Gaussian sub-bands V(red) and V(blue). (c) Time dependence of red and blue band with 3115 cm-1 pumping at different temperature.......................................................................................95 Figure 6.2.1 Experiment setup. (a) Experiment setup for ice/water related experiment. Different diffraction geometry and corresponding water diffraction image obtained on CCD camera in reflection diffraction setup and (b) transmission diffraction setup................................98 Figure 6.3.1 OH vibration modes of water. (a) Illustration of three vibration modes in OH bond of water. (b) Experimental observed frequency for OH vibrations in water [For 1968]. The corresponding wavelength for some frequency is listed in red........................................101 Figure 6.3.2 Different nonlinear process. (a) Geometry of sum-frequency generation. (b) Energy-level description of SFG. (c) Geometry of difference-frequency generation. (d) Energy-level description of DFG [Boy 2003].....................................................................................103 Figure 6.3.3 Optics path and setup for mid-IR generation. The green line indicates the 1256 nm optical path. Red line represents the 2165 nm laser path. The blue path is where the 3000 midIR travels. The M1 to M7 mirrors are purchased for the high reflection on 1256 nm and 2165 nm, while M8-M12 are Au coated exhibiting low loss for the infrared range. The purple arrows indicate the polarization of each wave................................................105 Figure 6.4.1 The water sublimation measured by from QMS as temperature rises with different dosing time..................................................................................................................................108 Figure 6.4.2 The pure silicon mounted on sample holder (a) before and (b) after water dosing. (c) Optical image of thin amorphous silicon membrane (blue area) manufactured on a silicon substrate (grey background). (d) Thin amorphous silicon membrane sample mounted (circled in red) onto our sample holder ready for transport into our UHV chamber for transmission diffraction experiments...........................................................................109 Figure 6.4.3 Pictures from water experiment. (a) The diffraction pattern from AuNP decorated silicon substrate at room temperature. (b) When the amorphous water starts to cover the AuNP and obscure the AuNP diffraction, water dosing can stop, taken at T = 115 K. (c) A few hours after water dosing is stopped, the amorphous water self-assemble into crystal form at 115 K. (d) Diffraction pattern from silicon with nanocavity at room temperature. (e) Scattering from water starts to replace the nanocavity pattern, taken at T = 78 K. (f) Fully crystallized water completely cover the Si substrate with nanocavity, taken at T = 127 K. (g) Diffraction pattern of ice yields to that from Si nanocavity when ice starts to sublimate at T = 157 K. (h) The diffusive diffraction pattern from amorphous silicon membrane at T = 115 K. (i) Diffraction pattern from ice and amorphous silicon membrane. (j) SEM image of nanocavity on silicon substrate.......................................110 xiv Figure 6.5.1 Reflective diffraction experiment on water. (a) Reflective diffraction geometry with ice deposited on pristine silicon and typical diffraction pattern from ice layer. (b) Intensity ratio dynamics of ice (111) + (200) triggered by 3000nm laser, f = 4.5mJ/cm2, at T = 130K.................................................................................................................................112 Figure 6.5.2 Transmission diffraction experiment on water. (a) Geometry of transmission diffraction experiment. (b) Diffraction profile obtained before (red curve) and 2 ps after (blue curve) the excitation laser hits the ice sample. The +2ps profile has been scaled to compare with that before mid-IR lands on sample.................................................................................113 Figure 7.1.1 Charge redistribution at interface after photoexcitation. (a) dielectric realignment. (b) carrier diffusion. (c) interfacial charge transfer..............................................................117 Figure 7.2.1 The slab model for transient surface voltage...................................................................119 Figure 7.3.1 Charge redistribution spectrum. (a) Surface photovoltage response map constructed using the diffractive voltammetry conducted on the water-ice surface covering gold nanoparticles/SAM/silicon interface at excitation wavelength from 400 to 800nm. Four selected surface photovoltage shown in white curves, at = 400, 470, 525, and 585nm, demonstrate a composition of two dynamics with different timescales. (b) comparisons between the surface voltage response spectra obtained from the interface without the coverage of water-ice (black line), ones with water-ice layer showing a red shift of the resonance peak (green line) at 30ps, and the bifurcation of peaks (blue line) at 100ps...................................................... .....................................................121 Figure 7.3.2 Dynamics of induced charge. (a) The controlled experiment with the presence of AuNP for Ice/AuNP/SAM/Si photovoltage measurement. The rise of the surface voltage is delayed by the timescale of the charge carriers migrating to the ice surface after being generated from the Si substrate. (b) Equivalent results obtained the surface with AuNP decoration. By comparing to (a), we can deduce the fast components (blue circles) unique to the nanoparticles-decorated surface.................................................................123 Figure A1 Analysis on electron count. (a) The discrete single-electron events recorded on a CCD camera. (b) The number of occurrences of single-electron events as a function of digital counts recorded for these events. A mean value of 989 is determined as the analogue-todigit unit, used to convert the CCD signals into the electron counts...............................128 Figure A2 Statistic on electron counts. (a) The data integration time used for each time stance under laser fluences F=2.43, 4.67, 7.30 mJ/cm2. (b) The absolute integrated intensity evolution of CDW superlattice peak in unit of electron counts. (c) The absolute integrated intensity evolution of main lattice peaks at (0,4) extracted from the same diffraction images as (b)................................................................................129 Figure B1 The zoomed in plot of satellite intensity of CeTe3 at early times showing two-step suppression. The data from F=2.43 mJ/cm2 are multiplied by 3 to compare with data from F=7.30 mJ/cm2. The error bars are calculated based on the counting statistics described in Appendix A...............................................................................................................130 Figure B2 Two component fit. (a) The results of two component fit of experimental S1(t)/ S1(t<0) data at F=7.30 mJ/cm2 (blue: total, red: first component, black: second component). (b) xv The value as a function of =A1/A2 based on fitting S1(t)/ S1(t<0)..........................132 Figure C1 Images of MWCNT. (a) Suspended MWCNT on copper TEM grid. (b) TEM image of a suspended MWCNT on TEM grid. (c) SEM image of a MWCNT deposited on holey carbon TEM grid. (d) SEM image of a MWCNT deposited on holey carbon TEM grid. (e) Diffraction pattern from a MWCNT. (f) Individually separated MWCNT on thin Si membrane................................................................................................134 Figure D1 Tsunami fs configuration.................................................................................................135 Figure D2 Two IR images on M4...................................................................................................136 xvi CHAPTER 1 Strongly Correlated Complex Materials Complex materials can be characterized as having no dominant energy scale; hence, the interaction between various degrees of freedom, like charge, lattice, orbital, and spin can greatly influence and determine their functionality. This strong interplay between subsystems often leads to emergent properties, like colossal magnetoresistance, high-temperature superconductivity, and spin- or chargedensity waves. To disentangle the coupling between these subsystems, ultrafast pump-probe techniques offer a glimpse of how the material responds after it has been disturbed. From the material response, we can learn the sequence, magnitude, and role of between each player in the system in such emergent properties. In this chapter, a survey of the literature on strongly correlated systems investigated by ultrafast technique is presented, sans the charge-density wave materials which will be reserved for Chapter two. 1 1.1. Colossal Magnetoresistance Manganites Magnetoresistance, the change of a material’s resistivity with the application of a magnetic field, was recognized more than 150 years ago, most notably by W. Thomson in 1856 [Tho 1856] when he measured the resistance of iron and nickel in the presence of a magnetic field. Later, in 1950, Jonker and van Santen found that the perovskite LaMnO3, an antiferromagnetic insulator, becomes metallic when La is substituted by Sr. When the substitution is around 30%, this hole-doped system displays an insulatorto-metal transition and ferro- to antiferromagnetic transition upon cooling [Jon 1950]. The application of magnetoresistance got a significant boost when giant magnetoresistance (GMR), a change in resistivity of more than 50% at low temperature [Bai 1988] or ~1.5% at room temperature [Bin 1989], was discovered by Albert Fert and Peter Grünberg. In the 1990s, R. von Helmolt et al. [Hel 1993] and Jin et al. [Jin 1994] coined the term colossal magnetoresistance (CMR) as they reported an orders-of-magnitude change in resistivity in manganite perovskites (Fig. 1.1.1). With the possibility of applications in magnetic field sensors, like those in hard disk drives, biosensors, and microelectromechanical systems, CMR remains a highly active field of research. In 1951, to explain the simultaneous occurrence of ferromagnetism and metallicity found by Jonker and van Santen, Zener proposed the “double exchange” mechanism, predicting the electron movement from one species to another can be facilitated more easily if the electrons do not have to change spin direction when on the accepting species. The electron’s ability to delocalize reduces its kinetic energy. The overall energy saving can lead to ferromagnetic alignment of neighboring ions [Zen 1951]. However, in 1996, Millis et al. [Mil 1996] and Roder et al. [Rod 1996] suggested the double exchange theory cannot explain the magnitude of change in resistivity at the ferromagnetic transition, and proposed that an electron-phonon coupling contribution, or a strong implied by the Jahn-Teller coupling, must be included in the Hamiltonian. To provide some insight on this discussion, Averitt et al. [Ave 2001] utilized ultrafast optical spectroscopy to show the relative contributions of spin fluctuations and phonons in determining the 2 (a) (b) Figure 1.1.1 Previous studies on CMR. (a) Magnetoresistance measurement at room temperature for LaBa-Mn-O thin films. (b) Temperature dependence of resistivity (R), resistivity (), and magnetization (M) of La-Ca-Mn-O films. conductivity in La-Ca-Mn-O and La-Sr-Mn-O ~100nm thin films. Using terahertz pulses to measure conductivity of the material after optical excitation, Averitt and coworkers observed a two-step transient response (Fig. 1.1.2). They attributed the fast, 2 ps, initial conductivity decrease to the change in phonon temperature as the optically excited electrons relax through electron-phonon coupling. To model the second step in the dynamics, they used a two-temperature model to describe the energy transfer between the phonons and spins after the initial increment of phonon temperature. The results from their two- temperature model were extended to quantify the contribution of the temperature change of spins and phonons to the change in conductivity (Equ. 1.1.1): 1.1.1 where Tp and Ts being temperature of phonon and spin while  being conductivity. From this analysis, they concluded the conductivity is primarily determined by thermally disordered phonons at low temperature while spin fluctuations dominate closer to Tc, as shown in Fig1.1.3(a). It has been shown that there is charge ordering in doped manganites, and this charge ordering has been interpreted as the localization of charge at atomic sites, or a “tolerance factor” involving the effect of 3 (a) (b) Figure 1.1.2 Previous studies on CMR. (a) Induced change in transmitted electric field. (b) Induced change in real conductivity. static crystal structure on electron hopping, as shown in Fig.1.1.3(b) [Mil 1998]. However, Cox et al. [Cox 2008] showed that the charge ordering in 0.5 doped La-Ca-Mn-O manganites has similar signatures of collective transport in impurity-doped charge-density wave (CDW) systems. From their observations under TEM, La0.5Ca0.5MnO3 has satellite peaks appearing only in the direction parallel to the superlattice direction, shown in Fig. 1.1.3(c). At the same time, resistivity measurements also show typical signatures of pinned and sliding states seen in anisotropic CDW systems, as shown in Fig. 1.1.3 (d) and (e). The similarity of electron-lattice properties between GMR, CMR and CDW materials shows the complex yet universal phenomenon in strong correlated electronic systems. 4 (a) (c) (b) (d) (e) Figure 1.1.3 Previous studies on CMR. (a) Contribution of spin and phonon to conductivity at different temperature (b) Phase diagram of La1-xCaxMnO3 showing phases including charge-ordering (CO), antiferromagnet (AF), canted antiferromagnet (CAF), ferromagnetic (FM), and ferromagnetic insulator (FI). (c) Line scan of TEM images in the a (red line) and c (blue line) showing the satellite peaks only present in the a direction. (d) and (e) Differential resistivity versus d.c. bias applied in the a (red lines) and c (blue lines) directions at various temperatures. 5 1.2. Cuprate Superconductors Similar to materials supporting CDWs, high-temperature superconductors (HTSC) are another class of strongly correlated systems in which the interplay between spin, charge, lattice, and orbital degrees of freedom play important roles. The division between CDW and HTSC systems became even more blurry when the charge-ordered “checkerboard” state was observed in cuprates [Han 2004], and when superconductivity emerged from a CDW material, 1T-TaS2 [Sip 2008]. With ultrafast techniques, the possible cooperation or competition between CDW and HTSC can be further explored. In 2007, Gedik and coworkers explored the superconducting phase transition in oxygen-doped La2CuO4+ with ultrafast electron crystallography [Ged 2007]. By observing the shift of diffraction intensity of a Bragg peak from one side of a point of constant intensity in momentum space to another, i.e., as for an isosbestic point, the spectral position where two interconverting species have equal absorbance, they attributed this phenomenon to a phase transition in which optical excitation induced a charge transfer from oxygen to copper in the copper-oxygen planes leading to lattice distortion, as shown in Fig. 1.2.1 (a). At the same time, by inducing this phase transition with optical excitation at different fluence, they observed that the photon-doping threshold, the number of absorbed photons per copper site, is very similar to the fractional charge per site required to induce superconductivity, as shown in Fig. 1.2.1 (b). This report demonstrated that ultrafast electron crystallography can be an ideal tool to explore phase transitions in strongly correlated systems. It also implied that optically induced carrier doping may be closely related to chemical doping, and hence signify the prospect of light-mediated control of phase transformations. In 2008, Kusar and coworkers utilized an optical pump-probe technique to study the energy landscape of the superconducting condensate in La2-xSrxCuO4. By observing the change of photo-induced reflectivity with different optical excitation fluence, they deduced the energy density required to vaporize the superconducting state is significantly higher than the thermodynamically measured condensation energy density. Together with the estimated spin-lattice relaxation time being orders longer 6 (a) (b) (c) (d) Figure 1.2.1 Previous studies on cuprates. (a) Diffraction intensity crossing a common point at different delay time at different fluence. (b) Threshold in fluence that would initiate the phase transition. (c) Typical photoemission data at Fermi surface showing change in electron dispersion and spectra after optical excitation. (d) Dynamics of superconducting gap magnitude at two locations. than the vaporization time observed in the experiment, they attributed the vaporization of condensate to phonon-mediated pair-breaking. Together with the work done by Torchinsky et al. [Tor 2013] observing the charge-density wave fluctuation in cuprate superconductors, it demonstrated that ultrafast optical pump-probe techniques may distinguish the pathways and mechanisms of phase transitions through spectral and dynamic information. Time-resolved angle-resolved photoemission spectroscopy (tr-APRES) was employed by Smallwood et al. in 2012 to investigate the Cooper pair recombination time at different locations of the superconducting gap in Bi2Sr2CaCu2O8+ [Sma 2012]. By observing the shift of spectral weight across 7 the Fermi surface, Smallwood and coworkers monitored quasi-particle creation and recombination at different momenta, as shown in Fig. 1.2.1 (c). Meanwhile, from the spectral peak shift, they deduced the dynamics of formation of the superconducting gap at different locations in the superconducting gap , shown in Fig. 1.2.1 (d). From these results, they suggested that the momentum-dependent recombination of Cooper pairs can be due to the quasiparticle energy and momentum approaching resonance with charge or spin density wave fluctuations. With tr-APRES, the dynamics at the Fermi surface can be readily explored, adding more information on the electronic correlations in the system. 8 1.3 Experimental Challenges Among the ultrafast techniques reviewed in the last section, ultrafast optical pump-probe techniques offer the high signal-to-noise ratio and relative ease of implementation. However, optical observations are often limited to the electronic response; hence, interpretation of the data can be difficult at times. While tr-APRES offers direct observation of electronic distributions in materials, it can be limited to information at the surface due to the relatively short penetration depth of low-energy electrons. Similar to optical pump-probe spectroscopy, tr-APRES offers only indirect observations of the lattice subsystem. Ultrafast X-ray diffraction techniques offer atomic information after optical excitation, however, it’s long penetration depth often limits the observation to bulk materials and relatively long experiment times. Ultrafast electron crystallography is suitable for obtaining atomic information, thanks to its sensitivity to lattice periodicity. Meanwhile, the typical nanometer-long penetration depth of highenergy electrons is ideally matched to the optical penetration depth for pump-probe studies. However, in order to obtain shortest time-resolution, it is crucial to have samples prepared with a high uniformity over similar length scales. 9 CHAPTER 2 Charge-Density Waves Materials This chapter presents some basics theoretical descriptions of charge-density waves (CDW) materials, the studies that investigate CDW with various techniques, and scientific open questions we wish to study and answer. Since the formation of CDW is the central argument in literature [Wil 1975] [Frz 1979] [Gru 1994], we would start the discussion with simple description on the electronic aspect of low dimensional system and the derivation of the Lindhard function in general. Then we discuss the instability in electron gas of low dimension, the related the phenomena like Kohn anomaly and Perierls transition, and the collective modes of CDW in brief. With an overview of past studies on CDW examined by various ultrafast techniques, we can discuss the results and implications from these previous works, as well as the prospects our ultrafast electron crystallography technique can bring to the discussion, and possibility provides some answers for some open questions. 10 2.1 Overview of Charge-Density Waves Charge-density waves can develop in low-dimensional metals due to the interaction between electrons and phonons. The resulting ground state exhibits a periodic charge density modulation with a periodic lattice distortion with both periods related by a wavevector that can be traced to Fermi- surface nesting [Grü 1994]. The CDW state originates from the reduced electronic dimensionality of the parent compound. Therefore we start with the simplest case, a one-dimensional metallic material, to introduce some basics of charge-density waves. 2.1.1 Nearly Free Electron in One-dimensional Conduction Band Using the free-electron model, where the only electron-lattice interaction is the electron confinement via the lattice to a 1D potential well, we can derive the electron dispersion relation, , as shown in Figure 1a, in terms of wavevector , electron mass (2.1.1) , and reduced Planck's constant . [Kit 2004]. However, in order to describe the electron properties better in various metals, semi-metals, or semiconductors, it is essential to include the weak perturbation of band electrons due to the periodic potential of the ion cores. This nearly free electron model can be rationalized by treating the valence electrons within a crystal as affected by diffraction from the lattice just as if they had been incident from the outside [Zim 1979]. In 1958, A.V. Gold first used this nearly free electron approximation, assuming that the conduction electrons are free except at the zone boundaries due to Bragg reflection from a periodic potential, to explain the band structure of lead, which has four valance electrons outside the filled 5d10 shell and 78 out of the 82 total electrons in the ion core [Gol 1958]. The band structure of nearly free electrons exhibits an energy gap at the zone boundary of the lattice, as illustrated in the first Brillouin zone in Figure 1b. With the Hamiltonian 11 , (a) (2.1.2) (b) Figure 2.1.1 Band structure of two electron models. (a) Energy versus wavevector for a free electron (b) Energy versus wavevector, or band structure, for an electron in a monatomic linear lattice of lattice constant [Kit 2004]. the magnitude of the band gap of the 1D nearly free electrons can be approximated by using as a perturbation the periodic lattice potential (2.1.3) where is the shortest wave vector in the reciprocal lattice, and matrix elements of is the lattice constant. The using a plane wave representation are (2.1.4) Using degenerate perturbation theory, we find the energy at the first Brillouin zone boundary k = π/a of the states and . The secular determinant is . 12 (2.1.5) Since at the boundary, Equation (2.1.5) reduces to or Hence the band gap at . (2.1.6) , is simply related to the periodic lattice potential (2.1.3) [Kit 1963]. The band gap calculated in this way, together with the nearly free electron assumption, provided a more accurate model for understanding insulator, semimetal, metal, and semiconductor. 2.1.2 The Lindhard Response Function of an Electron Gas For analyzing CDW materials, we shall examine the effect of a weak time-dependent potential acting on the free electron gas. experiencing an external potential We start with the Schrödinger equation for an electron : (2.1.7) In the case of , we have (2.1.8) where and volume of the system. The time-dependent perturbing potential is introduced as , (2.1.9) where the complex conjugate (c.c.) ensures no additional Fourier components are introduced and α→0+ enables the perturbation to be switched on adiabatically. The change in charge density and the perturbed potential can be related via the susceptibility where , (2.1.10) (2.1.11) and (2.1.12) 13 By applying the time-dependent first order perturbation formalism to (2.1.7), using , (2.1.13) and performing some rearrangements, we get (2.1.14) Using (2.1.9), we can expand the right-hand side of (2.1.14) as , (2.1.15) which gives us (2.1.16) and (2.1.17) With the wave function, we can determine the induced change in electron density: 2.1.1 2.1.1 b In (2.1.18a) to (2.1.18b), is the Fermi-Dirac distribution, and the spin degeneracy provides the factor of 2. We can also substitute is summed over all occupied with and with in the second term in (2.1.18b) since it values. This leads to 2.1.19 Comparing to (2.1.19) and (2.1.12), we obtain 14 (a) (b) (c) (d) Figure 2.1.2 Responses in different dimensions. (a) The Lindhard response function for different dimensions. (b) and (c) The Fermi surface, noted in red lines, and Fermi nesting, the condition of a common paring wavevector at the Fermi surface. (d) The pairs of one full and one empty state can be connected by the wavevector . 2.1.20 If we replace the summation with an integration and a static potential, or and , we obtain the following result 2.1.21 where is the dimension of the system. If we consider a 1D system with electron mass, and number of free electrons at length of the system, , (2.1.21) becomes the Lindhard response function, first derived in [Lin 1954], 2.1.22 2.1.2 15 2.1.24 where the density of states , Fermi energy , and Fermi wave vector with the assumption of a linear dispersion relation around the Fermi energy . For the case of when in (2.1.21), the two Fermi distributions in the numerator cancel out except or . This means the most significant contributions to the integral (2.1.21) come from pairs of occupied and unoccupied states, each of each of which has almost the same energy so that the denominator can be very small. Also, the paired states differ by so the Fermi distribution in the numerator does not cancel out, as illustrated in Figure 2.1.2(d). This divergence of at in 1D can also be observed in (2.1.24), which is plotted along with higher dimensional cases in Figure 2.1.2(a), known as Peierls instability [Pei 1956]. Together with equation (2.1.10), it implies that an external perturbation leads to a divergent charge distribution and suggests the electron gas itself is unstable with respect to the formation of a periodical electron charge distribution. The period of this charge variation is related to by 2.1.2 The divergence of the response function at can be related to the topology of the Fermi surface. For an extremely anisotropic 1D metal, the Fermi surface contains two lines that can be connected by a common wavevector , as illustrated in Figure 2.1.2(b), and is commonly referred to as perfect Fermi nesting. In this condition, the electrons can scatter efficiently into unoccupied states and change their wave vector by . However, in higher dimensions, as in the 2D Fermi surface shown in Figure 2.1.2(c) and the response function in a 3D case [Dre 02] plotted in Figure 2.1.2(a), 2.1.2 the number of paired states reduces significantly and thereby removes the singularity of 16 at . (a) (b) Figure 2.1.3 Low-dimensional gas. (a) Fermi surface of a quasi-one-dimensional electron gas [Grü 1994]. (b) The response function of a one-dimensional electron gas at various temperatures [Hee 1979]. In the case of a quasi-one-dimensional metal, like CeTe3 presented later in this thesis, the Fermi surface can be modeled by introducing a dispersion in the direction perpendicular to the direction along which the response function is evaluated [Grü 1994]. Starting from a two-dimensional dispersion relation 2.1.27 where a and b are the lattice constants in the x and y directions respectively, the quasi-one-dimensional dispersion relation close to the Fermi energy can be deduced by using and the linear dispersion in the x direction: 2.1.2 The Fermi surface obtained by calculating from (2.1.28), 2.1.29 exhibits a sinusoidal topology in the plane, as shown in Figure 2.1.3(a). Compared to the 2D case, the Fermi surface of a quasi-one-dimensional electron gas contains more electron pairs with similar energies, and the nesting condition is associated with the wave vector 17 . The response function exhibits a singularity at . In the two-dimensional phase space, the singularity corresponds to a periodic modulation with a wave vector and Perfect nesting condition in the quasi-one-dimensional case is possible only in the case when , and should be applicable to materials with strong anisotropy of the single particle bandwidth. As increases, the contribution from the third term in (2.1.29) becomes more significant and the singularity in is gradually removed, as illustrated in Figure 2.1.3(b). The temperature-dependence of the one-dimensional response function can be approximated linearly near , or around , by introducing with and to the numerator of (2.1.21), which yields 2.1. 0 This leads to 2.1. 1 2.1. 2 where is an arbitrarily chosen cutoff energy that is usually close to temperature dependence of . As in [Sol 2002], this finite in 2D can be derived by calculating the grand canonical ensemble of the structure function. The temperature-dependent response function suggests that we can expect a phase transition as the temperature crosses the Peierls critical temperature. 2.1.3 Instabilities in a One-Dimensional Electron Gas Relying on the notion that the external potential leads to a density fluctuation can examine various one-dimensional metasl by incorporating a potential in density , we induced by the change , 2.1. 18 States Pairing Total Spin singlet superconductor triplet superconductor charge-density wave spin-density wave electron-electron electron-electron electron-hole electron-hole Total Momentum Broken Symmetry gauge gauge translation translation Table 2.1.1 Various broken-symmetry ground states of one-dimensional metals [Dre 2002]. where is a -independent coupling constant, and and are the spatially dependent Fourier components of potential and density fluctuations, respectively. With (2.1.33) and replaced in (2.1.10), we obtain the induced density fluctuation 2.1. 4 From (2.1.34), we can see a system would reach an instability with a finite induced density fluctuation and when 2.1. For a rough estimate, we can plug (2.1.32) into and obtain the mean field transition temperature 2.1. Various fundamental condensates, e.g. superconductor, charge-density wave, and spin-density wave, present a stark contrast in sub-system interactions, paring of quasi particles and broken symmetry, yet many of their properties show similar presentation. It is vastly interesting to see that some materials, like 1T-TaS2 reported later in this thesis, can exhibit more than one condensate when conditions change. The occurrence of these states can be decided by a combination of electron-phonon interaction coupling constant and electron-electron interaction coupling constant momentum transfer of , which represent the interaction with and , respectively [Grü 1994]. Some of the properties of these broken- symmetry ground states are listed in Table 2.1.1. 19 The two superconducting states in Table 2.1.1 both develop in response to a interaction with total momentum , which is commonly known as particle-particle channel or Cooper channel. With a pairing that results in total momentum , it produces the charge-density wave or spin-density wave via the particle-hole channel, or the Peierls channel. For all these condensates, the order parameter is complex, 2.1. 7 For superconducting states, the gauge symmetry is broken while the phase is invariant under a gauge transformation. On the other hand, the two density-wave ground states exhibit broken translational symmetry. The collective excitations of these two density-wave ground states are called phasons and amplitudons, as they are related to changes in the phase and amplitude, respectively,m of the condensate order parameter. The amplitude is related to the single particle gap that appears at in the case of density waves [Grü 1994]. 2.1.4 The Kohn Anomaly and the Peierls Transition In order to describe the charge-density wave and its transition, a Hamiltonian that includes the electron-phonon interaction is needed. For this purpose, the Fröhlich Hamiltonian [Fro 1954] is commonly used. Here it is written in the second quantization formalism 2.1. The first term in (2.1.38), the Hamiltonian annihilation operators, and for the electron gas, includes the creation and respectively, for the electron state with energy phonon system is described by the second term in (2.1.38), annihilation operators and . The , with the phonon creation and , characterized by the wavevector . In terms of these operators, the lattice displacement can be expressed as 20 2.1. 9 where is the number of lattice sites per unit length, is the ionic mass, and is the normal mode frequency. At the same time, the normal coordinates of ionic motion can be described by 2.1.40 Finally, the third term in (2.1.38), which represents the electron-phonon interaction , contains the electron-phonon coupling constant [Grü 1994] 2.1.41 With the Fröhlich Hamiltonian (2.1.38), we can describe the effect of the electron-phonon interaction on the phonon frequency by establishing the equations of motion of the normal coordinates. With a small displacement in coordinate, the equations of motion read and where 2.1.42 is the second time derivative of the coordinate. Utilizing (2.1.10) and the commutation relations of the normal coordinates and conjugate state momenta of the ionic motions, (2.1.42) becomes 2.1.4 where is the phonon frequency without electron-phonon interaction. From the equation of motion (2.1.43), the renormalized phonon frequency is 2.1.44 The phonon frequency depends on the interatomic restoring force, which originates from Coulomb interaction between the cores, for the corresponding lattice arrangement. When the lattice distortion provides the electronic system with a potential, it induces charge redistribution, as presented earlier in section 2.1.2. It is reasonable to imagine the induced charge-density wave reduces the restoring 21 (a) (b) Figure 2.1.4 The Kohn anamaly. (a) The Kohn anomaly of acoustic phonon frequency showing the Kohn anomaly at temperatures above the mean field transition temperature. (b) Phonon dispersion relations of 1D, 2D, and 3D dimensional metals [Grü 1994]. force between cores through shielding effects. Therefore the phonon frequency should reduce, or soften, known commonly as Kohn anomaly. By incorporating (2.1.32) as , the phonon frequency becomes (2.1.45) As temperature decreases, , and we obtain the transition temperature at which the phonon frequency is "frozen-in", or the Peierls charge-density wave transition temperature in the mean field approximation, 2.1.4 Where is the electron-phonon coupling constant [Grü 1994] 2.1.47 When Taylor-expanding (2.1.45) at , we can determine the temperature-dependence of 22 as for 2.1.4 Using (2.1.44) and (2.1.48), we can plot the phonon dispersion relation showing the emergence of the "frozen-in" phonon as in Figure 2.1.4(a). The phase transition is defined by the temperature where , caused by the sharply diverging response function of the 1D electron gas. For higher dimensions, however, the reduction of phonon frequency is less significant, as shown in Figure 2.1.4(b), and temperature. Therefore, for a weak electron-phonon coupling, is less dependent on the can remain finite at and there is no phase transition. Below the phase transition temperature , the renormalized phonon frequency is zero, leading to the “frozen-in” lattice distortion. Macroscopically, this means the occupied phonon mode has finite expectation values . Therefore, we can define the order parameter (2.1.37) as 2.1.49 Combined with (2.1.39), we get [Grü 1994] 2.1. 0 with 2.1. 1 This means the increment in the elastic energy due to the lattice distortion can be expressed as 2.1. 2 or, when plugging in (2.1.50), 2.1. where is defined in (2.1.47). The Fröhlich Hamiltonian (2.1.38) becomes 23 2.1. 4 When considering and , the Hamiltonian can be expressed as 2.1. The electronic part of (2.1.55) becomes, with order parameter (2.1.49), 2.1. With the dispersion relation the states near and near , we consider only the states near Fermi level, and label with subscript 1 and 2 respectively. The electronic part of Hamiltonian can be written as 2.1. 7 where substitutes for simpler notation One can use Bogoliubov transformation, typically used in BCS theory, to diagonalize (2.1.57) with a new set of operators and Using the constrain of 2.1. , (2.1.57) becomes 2.1. 9 It can be diagonalized if the coefficient of off-diagonal terms is zero, or 2.1. 0 We can satisfy the constrain by choosing and 2.1. 1 which leads (2.1.60) to 2.1. 2 24 (a) (c) (b) Figure 2.1.5 The single particle band, electron density, and lattice distortion in (a) state above and (b) in CDW state at . (c) The temperature dependence of band gap and the renormalized phonon frequency . Both carries a characteristic dependence of Plugging (2.1.62) into (2.1.61) then we get [Grü 1994] and 2.1. where 2.1. 4 Substituting (2.1.63) in (2.1.59), we obtain 2.1. At the same time, the ground-state wave function can be written as 2.1. where represents the vacuum. The periodic charge density variation can also be calculated in the weak coupling limit [Grü 1994]: 25 2.1. 7 where is the constant electronic density in the metallic state. The equilibrium lattice positions (2.1.50), the dispersion relation (2.1.64), and the electronic density (2.1.67) are shown in Figure 2.1.5. Instead of the linear dispersion of a metallic state, from (2.1.64) and (2.1.65) we can see the electron density of states disappears in the CDW ground state and an energy gap opens at the Fermi level, . The 1D CDW material can become an insulator upon the gap opening, but the 2D materials stay metallic due to the ungapped region of the Fermi surface [Folge 1973] [Ru 2008]. The ground state, depicted in Figure 2.1.5(b), exhibits a periodic modulation of the electron density, as well as the lattice position distortion, hence the term ChargeDensity Wave. By minimizing the energy of (2.1.64), we can obtain the magnitude of the gap. The gap opening lowers the electronic energy, which can be calculated by 2.1. 2.1. 9 By expanding the log term in the weak coupling limit, , (2.1.68) becomes 2.1.70 Combing (2.1.53), the total energy change in the CDW ground state is 2.1.71 If we minimize the total energy with a weak electron-phonon coupling, or , we obtain 2.1.72 Comparing with (2.1.36), we get [Grü 1994] 26 (a) (b) (c) Figure 2.1.6 CDW states. (a) CDW ground state (b) Phase mode (c) Amplitude mode. The dotted lines represents the electronic part of charge-density wave while the arrow indicates the displacement of ion core, as red dots, from the equilibrium position. 2.1.7 At the same time, the condensation energy 2.1.74 Equation (2.1.73) follows the BCS relation between zero-temperature gap and the transition temperature. At , thermally excited electrons can cross the band gap, screen the electron-phonon interaction, reduce the energy gain, and eventually induce a phase transition. The temperature evolution of the gap near , shown in Figure 2.1.5(c), can be derived [Tin 2004] as 2.1.7 The equation (2.1.73) is essentially the same as that describing the temperature dependence of the superconducting gap using the framework of BCS theory [Sch 1964] [Tin 1975]. 2.1.5 Collective Excitation of Charge-Density Waves The charge-density wave excitation can be described by a complex order parameter (2.1.37), therefore amplitude and phase modes should be expected. In the at limit, two phonon dispersion relations of the charge-density wave have been derived by [Lee 1974]: and where 27 2.1.7 2.1.77 The two excitations in (2.1.76) are commonly referred as phase mode (phason) and amplitude mode (amplitudon), and are sketched in Figures 2.1.6(b) and (c), respectively. When the phason and , the CDW collective excitation corresponds to a translational motion without dissipation, which is known as the mechanism of Peierls-Fröhlich superconductivity. However, this phenomenon is limited by impurities in the lattice, or the pinning effect. Since in the phase mode, the displacement of electronic charge distribution relative to the ionic positions is involved, the phason is expected to be optically active. In contrast, this displacement is absent in the amplitude more. Therefore amplitudon should be Raman active [Grü 1994]. 28 2.2 Charge-Density Waves Investigated by Various Techniques and Scientific Outstanding Questions Thanks to advances in ultrafast lasers and pioneering work that developed the technique [Zew 1990], femtosecond time-resolved spectroscopy has been a new tool for studying the interplay, transformation, reaction, and relaxation between lattice, charge, and spin degrees of freedom. The interconnected order parameters, or the modulation of charge density is accompanied with the modulation of the underlying lattice, presents a various degree of cooperativity that is crucial in the phenomena in strongly correlated systems. Numerous all-optical femtosecond time-resolved experiments have been performed on CDWs [Dem 1999] [Dem 2002] [Shi 2007]. The Mihailovic group reported temperature-dependence of the single-particle dynamics of electron-hole recombination, amplitude mode oscillations, and phase mode damping time scale for the first time in an ultrafast reflectivity study on K 0.3MoO3 [Dem 1999]. In the relaxation of the femtosecond-laser-induced jump in reflectivity, they observed the two components distinguished by their different time constants, and , in the dynamics (Fig. 2.2.1a) and attributed them to phase mode damping and the recombination of single particles (SP), respectively. From the temperature-dependence , they suggested the existence of a single-particle gap. Similar work was also performed again on 1T-TaS2 and 2H-TaSe2 by the same group in 2002 [Dem 2002], and based on the slower relaxation, shown in Fig. 2.1.1(b), when the excitation energy is less than the full gap, they suggested a dynamically inhomogeneous intermediate state local precursor CDW segments to appear on the femtosecond time scale. In 2007, Shimatake and coworkers reported similar finding in NbSe 3, a material exhibiting two independent CDW transitions that occur with different nesting conditions in k space [Shi 2007]. Another femtosecond time-resolved technique is angle-resolved photoemission spectroscopy (trARPES) that ejects the electrons from the material via photoemission and allows the observation 29 (a) (c) (b) (d) Figure 2.2.1 Previous studies on 1T-TaS2. (a) The time evolution of normalized reflectivity measured at different sample temperature, T = 45 and 110 K displayed in log scale to highlight the two time scale in relaxation [Dem 1999]. (b) the temperature dependence of relaxation time of 1T-TaS2, plotted with result taken upon warming in open symbols and cooling in solid symbols [Dem 2002]. (c) Dynamics of Hubbard peak normalized intensity of 1T-TaS2 in Mott-insulator state [Per 2006]. (d) Shift of the Hubbard peak that recovers in ps time scale [Per 2006]. of the density of states at different momenta, effectively mapping the band dispersion and Fermi surface. Since the Fermi surface topology plays an important role in CDW formation, the direct observation of the CDW bandgap and nesting condition provides valuable information. Using static ARPES, V. Brouet and coworkers determined the Femi surface topology of CeTe3, shown in Fig. 4.1.3 (b), correlating the folded part of the Fermi surface directly to the weak coupling between the lattice planes with poor conductivity, which contributes to the 2D nature of the material [Bro 2004]. Utilizing tr-ARPES, Perfetti and coworkers observed a 100 fs collapse and sub-ps recovery of the Hubbard band in the Mott-insulating 30 state of 1T-TaS2, shown in Fig. 2.2.1 (c). They also reported a long, 9.5ps recovery correlated to the phonon relaxation [Per 2006]. In 2008, Schmitt and colleagues observed similar fast recovery of the electronic part at the CDW bandgap and lingering lattice vibrations after an intense femtosecond excitation [Sch 2008]. All these ultrafast optical pump-probe techniques focuses on the observation of the electronic part of the CDW. These studies consistently present an outstanding puzzle regarding the identification of a sub-ps partial recovery of electronic ordering being independent of the perceived underpinning mechanism. This universality may be explained by the lattice being frozen in its modulated state on the sub-picosecond time scale, but there has been no direct proof of this hypothesis. The sole atomically sensitive study was reported by Eichberger and colleagues using an ultrafast electron diffraction observation on 1T-TaS2 [Eic 2010]. However, this study only examined the dynamics of the CDW without inducing a CDW phase transformation. Hence, the implications of the result are limited. Together with the capability of direct observation of ultrafast structural evolution of a CDW and the lowvibration cryogenic sample holder, we are poised to provide a complementary view to the mechanism of CDW formation and to explore the energy landscape of CDW phase transitions. 31 CHAPTER 3 Ultrafast Electron Crystallography Techniques for Studying the Low-Dimensional Material CeTe3 In this chapter, a brief introduction of electron diffraction theory is presented first to provide a basic understanding of the phenomenon of diffraction. This is followed by the sample preparation and characterization developed specifically for low-dimensional materials. During the development of the sample preparation technique, we realized that having high-quality, well prepared samples is one of the cornerstones for a successful experiment. Finally, in this chapter, we will briefly describe the experiment setup of our UEC technique. 32 3.1 Diffraction Theory Diffraction has been one of the most powerful techniques providing structural and compositional information of materials. Since diffraction theory was developed originally using X-rays [Lau 1914] [Bra 1915], the majority of the crystallographic information we have about materials are obtained by X-rays. However, Louis de Broglie proposed the wave-particle duality [Bro 1924] in his PhD thesis, which paved the way for the development of electron diffraction [Dav 1927] [Tho 1928]. X-rays interact with the electrons in a system, and it is the emission by these electrons of their own electromagnetic field, identical to the incident X-rays, that creates the resultant field-to-field scattered wave. In comparison to X-rays, electrons are scattered much more strongly, as they interact with the electromagnetic field of both electrons and nuclei in the material, and these incident electrons are scattered directly by the target sample. It is these attributes that allow electron diffraction to be used specifically for measurement of surfaces or minute samples to determine the periodic structure of crystals, stacking faults, displacements, impurities, et cetera. In the situation in which a large, high quality specimen is hard to come by or the material of interest is of nanometer size, electron diffraction plays an important role in revealing structural information. 3.1.1 Diffraction Condition The de Broglie wavelength can be calculated by (3.1.1) where can be expressed as the kinetic energy and rest energy of electron via (3.1.2) that gives us , 33 (3.1.3) (a) (b) Figure 3.1.1 Diffraction. (a) Elastic scattering from two planes consisting identical atoms. Vectors ki and kf are the incident and scattered wave vectors. (b) Momentum transfer, s, being the vectorial change of incident and scattered wave vector, while θsc is the angle between incident and scattered wave vectors. where can be calculated from the acceleration voltage applied to the electron, electron, is the mass of is the Planck's constant, and is the speed of light. For the typical 30 keV electron used in our UEC experimental setup, the associated wavelength is = 7.0 pm. This shows that UEC is the ideal tool for studying material on the nanometer scale. Consider the incident wave of an electron beam striking two planes of identical atoms that are separated by , and the final wave after electron scattering from the material, as shown in Figure 3.1.1(a). The diffraction intensity of the scattered wave on a screen in the far field is maximum if these waves are constructively interfering. Namely, they exhibit a path difference of where an integer that denotes the order of diffraction. In a simple condition when , the path difference of two adjacent waves is is and the maximum diffraction intensity occurs when (3.1.4) which gives us the Bragg condition that relates the lattice distance , the scattering angle , and the wavelength of the propagating wave . To generalize the scattering process, we use the momentum transfer, wavevector of incident or scattered waves of the process, illustrated in Figure 3.1.1. 34 where With the is the and being the incident and scattered angles, respectively, the path difference of the same wave front scattered from two adjacent scatterers is , (3.1.4) and the phase difference of the scattered waves is (3.1.5) which can be written in terms of the wavevectors .1. where . In the condition where the phase difference is , or the Laue condition, we expect the maximum diffraction intensity when waves interfere constructively. For a 30 keV electron, the scattering is essentially elastic, or . With this condition, the momentum transfer , figure 3.1.1(b), can be expressed as or .1.7 Using the Laue condition, (3.1.7) can be reduced to the Bragg condition (3.1.4), or .1. 3.1.2 Scattered Intensity In a general scattering event, Figure 3.1.2(a), the scattering intensity recorded at the detector can be expressed as the differential scattering cross section [AN 2001] .1.9 35 (a) (b) Figure 3.1.2 Scattering process. (a) Generic schematic layout and notation of scattering process. (b) An electromagnetic plan wave polarized with its electric field along the z axis forces an electric dipole at the origin to oscillate [AN 2001]. where is the distance between scattering object and the detector, the solid angle, beam, and is the scattering cross section, is the scattered intensity recorded at the detector, and is is the strength of the incident are the radiated and incident electric field, respectively. In the case of X-ray scattering, one can use the dipole approximation of the scattering of the electric field by an electron, Figure 3.1.2(b), and the radiated over incident ratio can be derived as .1.10 where accounts the polarization factor, is the incident wavevector, and is the fundamental length scale, or Thomson radius: .1.11 Therefore, the differential cross section for X-rays can be calculated as .1.12 36 (a) (b) (c) Figure 3.1.3 X-ray scattering event from (a) an atom, (b) a molecule, and (c) and a crystal [AN 2001]. When considering X-ray scattering from an atom with Z electrons, one can consider that a volume element factor of at would contribute an amount of , where and to the scattered field with a phase being the number density. Hence the total scattering length of the atom can be expressed as [AN 2001] .1.1 where is the atomic form factor for the X-ray scattering. Compared to X-ray scattering, which assumes the electron charge density is spherically distributed, electron waves scatter coherently (Rayleigh scattering) from tightly bound electrons in the atom as well. Therefore, to determine the electron scattering from an atom, one can calculate the electron atomic form factor from the X-ray form factor using the Mott-Bethe formula [Kir 2010], .1.14 where is the electron atomic form factor, is the Born radius, and Z is the atomic number of the atom. When considering molecule or crystal scattering, however, the structure factor for the X-ray or electron, after normalizing by the form factor, appears to be the same. Therefore the formalism of scattering is interchangeable. When considering a molecule, Figure 3.1.3(b), the scattering can be written as [AN 2001] .1.14 37 where is the atomic form factor of the jth atom in the molecule, and a factor similar to that in (3.1.13) is needed when calculating the intensity in absolute units. Finally, for a crystal assembled by periodically spaced molecules, the scattering amplitude factorizes into two terms, .1.1 where the first term is the unit cell structure factor and the second one is the lattice sum. For a crystal which is defined as a material that is periodic in space, we can describe the position of every atom by , where specifies the origin of the unit cell and is the position of the atom relative to that origin. The new aspect in (3.1.15) is the lattice sum. Each term in that sum is a complex number which will contribute to most when all the phase terms satisfy .1.1 This condition makes the lattice sum equal , the number of unit cells. The lattice vectors have the form .1.17 where are integers and are the basis vector that define the unit cell. A solution to (3.1.16) can be found by introducing a reciprocal lattice spanned by basis vectors .1.1 so that any lattice site in the reciprocal space can be written as .1.19 where are integers. From (3.1.17) and (3.1.19), we can see .1.20 which leads to the conclusion that .1.21 38 This shows that is finite if and only if coincides with a reciprocal lattice vector . This is known as the Laue condition. Hence the scattering from a crystal is confined to distinct points in reciprocal space. Consider a small crystal constructed with scatters spaced with dimensions where are the numbers of unit cells in the respective direction. From (3.1.15), for a 3D crystal we obtain .1.22 .1.2 where each sum is a geometric series that can be rewritten as .1.24 Therefore, the experimentally observable scattering intensity is .1.2 which shows the scattering intensity is proportional to occurs at . Meanwhile, since zero diffraction intensity , the width of the diffraction peak is proportional to . Hence, within the penetration depth of our incident electron, we can obtain much stronger and sharper diffraction patterns if we can include more scattering sites, or molecules, in the diffraction process,. 3.1.3 The Debye Waller Effect At room temperature, the atoms in a crystal exhibit random thermal vibrations with an amplitude on the order of m. Even at , atoms still perform oscillations. These atomic vibrations can be tracked as an ensemble of lattice distances sampled through diffraction. Depending on the statistics of 39 the ensemble distribution, one can establish a relationship between the degree of vibrations and the diffraction intensity, as discussed below. The atom's position can be extended from the static position by a time-dependent displacement in a form .1.2 By replacing with (3.1.26) in time-averaged (3.1.14), we have .1.27 .1.2 where is typically called the static structure factor. The exponential term in (3.1.28) can be Taylor-expanded into .1.29 Since and the geometrical average of over a sphere is , (3.1.29) becomes .1. 0 Therefore, the experimentally observed diffraction intensity can be expressed as .1. 1 where the exponential part is commonly referred to as the Debye-Waller factor. Since potential energy , we get .1. 2 Therefore, (3.1.31) can be expressed in a temperature-dependent form .1. 40 In our UEC experiment, the sample is excited with a laser and the lattice temperature should elevate after optical excitation. Using (3.1.33), we can expect the relationship between the diffraction intensity before, and after, the laser illumination on sample to be .1. 4 The higher order reflection, or diffraction peak at larger values, show stronger effects due to changes in lattice temperature. 41 3.2 CeTe3 Sample Preparation and Characterization High quality CeTe3 crystals were grown by our collaborator, Christos D. Malliakas in Prof. Kanatzidis group at Northwestern University. All manipulations were carried out under dry nitrogen atmosphere in a Vacuum Atmospheres Dri-Lab glovebox. Cerium (~ 0.3 g, 99.9% pure, filling from ingot, Chinese Rare Earth Information Center, Inner Mongolia, China) and tellurium (~ 8.8 g, Plasmaterials, at 99.999% purity) were loaded into fused silica tubes of 12 mm diameter under inert atmosphere. Then each tube was inserted into a 15 mm fused silica tube and a stainless steel mesh filter was placed atop it. A small segment of fused silica tubing was used as a counterweight to keep the filter in place during centrifugation. The tubes were flame sealed under vacuum (<10 -4torr) and heated to 900 o C at 24 hours for 1 day and cooled down to 650 oC in 5 days. Tubes were removed at 650 oC and centrifuged to remove the Te flux. The morphology of the crystals is that of thin plates with a brown (copper-like) color. After confirming the crystals were indeed high purity CeTe3 using EDS and X-ray, the raw materials were sealed in a glass tube under vacuum then sent to our group for further sample preparation. In order to have sufficient electron to penetrate through the CeTe3, the sample has to get thin down to below 100nm in thickness at an area that is at least the same size as our electron beam footprint, typically ~30um. Following the guidance from Dr. Xudong Fan at Center for Advanced Microscopy, we first waxed the single crystal CeTe3 bulk sample on to a stud, and then flattened it on one side with diamond lapping film (1-5µm Diamond Lapping Film from Electron Microscopy Sciences, Cat. # 50350) using water as lubricant. When one surface was flattened, the sample was glued (Vishay Micro- Measurements M-bond 610) to a Transmission Electron Microscopy (TEM) slot grid (Ted Pella) to have the other surface polished (Figure 3.2.1a). During the polishing, the sample was waxed on a stud and pressure was applied by a custom grinder (Figure 3.2.1b). When the sample thickness was less than -milling (Gatan 691, Figure 3.2.1c) process until light penetrated the sample. During ion-milling process, we used 3 to 4 kV ionic Argon flow and incident 42 (a) (b) (c) Figure 3.2.1 Equipments for sample preparation. (a) CeTe3 sample glued to the copper grid. (b) Custom grinder for thinning the sample. (c) Gatan 691 Ion Milling Machine. angle of less than 5 degree. The sample was rotating at 3 to 4 rpm when ion-milled, and the whole ionmilling process took more than 10 hours in total before an edge was created on the sample surface. The quality of the ion-milled sample was first checked with a TEM (JEOL 2200FS, 200kV). The TEM image of CeTe3 sample (Figure 3.2.2a and b) showed a wide and thin area of material ideal for UEC experiment. The TEM diffraction image (Figure 3.2.2c) showed clear satellite reflections (S1) along the c* axis, which are circled in red, together with the much brighter main Bragg reflections (S0) with square-symmetry, circled in blue. The relatively high intensity of satellite peaks confirmed the large and high quality of the raw material made by our collaborator. Electron microprobe energy dispersive spectroscopy (EDS) was also performed on several crystals of the compound and confirmed the 1:3 ratio of the Cerium to Tellurium (Figure 3.2.2d). The thickness was estimated to be ~50nm using Electron Energy Lost Spectra (EELS) of The JEOL TEM. The estimated sample thickness was calculated using the integration of EEL spectrum [Lea, 1984] that extrapolated the ratio of thickness t over the characteristic mean free path λ in material from the log ratio of the total number of electrons It in EELS and that of electrons having no energy lost I0 (Equation 3.2.1), 43 Figure 3.2.2 TEM observation on CeTe3. (a) Ion-milled opening at CeTe3 sample. (b) CeTe3 film at the edge of the opening. The central dark spot is a burn mark on the CCD camera. (c) TEM diffraction image of CeTe3. The satellite peaks appear on the two sides of the Bragg reflection along c* direction (circled in red), while the main Bragg peaks, circled in blue, show square-symmetry along both a* and c* axes. (d) EDS element analysis of CeTe3 sample showing ~1:3 ratio of Ce:Te. The Carbon trace was contributed to the diamond lapping film used in the initial thinning of sample. The Copper trace was originated from the cooper TEM grid the CeTe3 was glued on. t I = ln I t 0 (3.2.1). The number of total electrons and zero-energy-lost electrons was linearly proportional to the intensity of TEM transmission pictures taken without energy filter (Figure 3.2.3a) and that with energy filter that blocked out energy-lost electrons (Figure 3.2.3b), respectively. Using these two pictures, the TEM camera software produced the thickness map (Figure 3.2.3c) that intensity of each pixel is equal to ratio of sample thickness t over the mean free path λ. The mean free path λ was calculated to be 92.58 ± 18.52nm, using the formulation derived by Malis, et al. [Mal 1988], 44 (c) (d) (e) Figure 3.2.3 Thickness map on CeTe3. (a) TEM picture taken without energy filter. (b) TEM picture taken with energy filter that blocks out energy-lost electrons. (c) Thickness map processed using (a) and (b). The scale bar in (c) also applies to (a) and (b). (d) Typical EELS from CeTe3 material. (e) Thickness profile of ion-milled CeTe3. (3.2.2) , E0 is the energy of incident electron in keV, Em is the weighted average of energy lost of electron, and β is the spectrum collection semiangle in mrad. From the EEL spectrum (Figure 3.2.3d) of our CeTe3 sample, Em is averaged from the 3 FWHM of the zero-lost peak as the lower limit to the end of spectrum, 100eV. This relativistic factor F was 0.0618 for 200keV incident electron, and β is 10mrad, according to the manufacture of our TEM. By averaging the intensity of a 0.5um wide area in thickness map (highlighted area in Figure 3.2.3c) and calculated λ, we obtained the thickness profile of our ion-milled 45 CeTe3 sample respect to the distance from the edge of opening. From the method mentioned above, our CeTe3 sample was estimated to be 20 - 80nm thick within 0.5µm from the edge of opening (Figure 3.2.3e), which translated to 5.7 degree sample slope that is very close to the 5 degree incident angle of ionic Argon during ion-milling process. 46 3.3 Experimental Setup We perform ultrafast electron crystallography (UEC) in an ultrahigh vacuum chamber (Figure 3.3.1a) equipped with a custom goniometer to allow the experiment to be conducted in either reflection or transmission geometry. In this technique, femtosecond photoelectron pulses are used to replace the optical probe in the traditional all-optical pump-probe experiments to provide structural information on the excited state following laser pulse excitation. The femtosecond electron pulse is generated at a silver photocathode using 266 nm laser pulses produced by tripling the fundamental 800 nm 50 fs laser pulse, which is also used as the optical pump to excite the sample. To minimize the temporal broadening of this electron pulse due to space charge effects, a proximity-coupled cathode-lens assembly is employed (Figure 3.3.1b). The electron pulse is accelerated to 30keV within a short distance of 4mm, collimated first using a front aperture and allowed to pass through a magnetic lens running current at 320 ampereturns. The magnetic lens focuses the pulsed electron beam and the beam is further trimmed by a replaceable exit aperture before intercepting the sample, which is typically 5cm away from the cathode. The probe size can be controlled via adjusting the focusing strength of the magnetic lens or employing different exit apertures, and ranges from 5 to 20 µm. The probe size is characterized in situ via a sharp knife-edge technique. The temporal resolution of the UEC experiment is typically determined by the condition of pump-probe overlap. In the reflection geometry, since the electron footprint is elongated along the incidence direction by a factor of 1/sin θi , where θi is the incidence angle, the typical resolution is around 1 ps due the velocity mismatch over the stretched probed region (~ 100 µm with incidence angle of <5°). In the transmission geometry, the probe size is in the 10 µm range, so the temporal resolution is ultimately controlled by the probe electron pulse, which is space-charge-limited. We have characterized the space charge effects through imaging the real-space longitudinal electron pulse-length by shadow-imaging technique [Tao 2012]. We establish a power-law growth of electron pulse-length due to space charge effects, which can be used to chart the pulse-length of the electrons for a broad range of electron counts per pulse, as shown in Figure 3.3.2a. For this experiment, we kept the electrons counts to 47 (a) (b) Figure 3.3.1 Experiment setup. (a) Layout of ultrafast electron crystallography apparatus. (b) Schematic diagram of the proximity-coupled femtosecond electron gun. be ~800 e- per pulse, the best estimate of the pulse-length is 390±110 fs (at FWHM). To establish the pump-probe spatial and temporal overlaps prior working on the CeTe3 sample, we use the reaction of a graphite sample that is mounted near the sample. First, we characterize the pump laser profile by scanning the laser across the fine electron footprint on graphite surface and record the opto-electrical response from the diffracted beam, from which we can determine Zero-Of-Time (ZOT), or the time when pump and probe both arrive at the sample, to be within 500 fs [Rua 2009]. The timing between the pump and probe pulses is adjusted using an optical delay stage in the optical path of the pump laser. For this CeTe3 experiment, the transverse width (at FWHM) of the excitation laser is determined to be 00 μm and is stretched along the beam direction to 0 μm considering the 4 ° incidence angle. Following the alignment, the CeTe3 sample is moved to the location of the pump-probeoverlap, labeled on the screen of a CCD camera, and the overlap can be verified from the transient response of on CeTe3. At the same time, The transmission electron diffraction pattern of CeTe3 obtained using UEC apparatus is shown in Figure 3.3.2b. Because of the disparity in S0 and S1 intensities, in order to record the Bragg and satellite reflections simultaneously, UEC experiment is performed at an exposure time 48 (a) (b) (c) Figure 3.3.2 Experiment setup. (a)The electron pulse-length as a function of the number of electrons per pulse employed. (b) Diffraction pattern of CeTe3 obtained from UEC setup. where the main Bragg peak will reach 2/3 of the saturation level of our CCD camera, and frame-averaged over 200 diffraction images to obtain an averaged time-resolved diffraction image at each time stance with sufficient signal-to-noise level to quantify both S0 and S1 changes. Because of the smaller Ewaldsphere at 30 keV (compared to TEM experiment), we slightly tilt the crystal along the a-axis to optimize the intensity of the satellites along the (3,x) –stripe, as shown in Figure 3.3.2c, where satellites appear most visibly at (3,±Q0) and (3,2±Q0) and are well separated from the Bragg reflections. 49 CHAPTER 4 Structural Dynamics of Charge-Density Waves CeTe3 is the first charge-density waves material our group study on. We are intrigued by its unique uniaxial CDW formation that stands out among the already exotic charge-density waves material. In this chapter, we first discuss the special property that gather much interests from other scientists. Then we present the finding obtained from our experiment on CeTe3 and how we utilize its rare property to provide information that other CDW material cannot. 50 4.1 Background on CeTe3 In the first experiment designed to probe the fluctuational dynamics of CDW, we choose to investigate CeTe3 that belongs to the Rare Earth tritellurite system (RETe3), which is well regarded as a model system to investigate 2D CDW formation, and can be quasi-continuously tuned by varying the RE element. The novelty of this system is in its 2D non-correlated nature where all the steady-state measurements seem to suggest it to be a rare case beyond 1D where the standard Peierls mechanism actually applies [Bro 2004]. In the case of CeTe3, the weak electron correlation effect along with the uniaxial CDW formation in a Te square lattice makes it ideal for studying symmetry breaking phase transition in 2D. In 1995, DiMasi and his colleagues first reported the CDW in RETe3 by transmission electron microscopy [DiM 1995]. The CDW ground state has been studied with various techniques like APRES [Bro 2004] [Shi 2005] [Gar 2007] [Bro 2008], variable temperature x-ray diffraction [Mal 2005] [Ru 2008], Raman scattering [Sac 2006] [Lav 2008], STM [Fan 2007], and susceptibility, heat capacity, and electrical resistivity measurements [Ru 2006]. By substituting the rare earth element in RETe 3 with heavier one in the family, one can decrease the lattice parameters caused by Lanthanide contraction, which is originated from the increasing screening of the core electrons with increasing number of 4felectrons [Ru 2008]. This effect leads to the increment of the wave function overlap, which increases the electron density at the Fermi level , shown in Figure 4.1.1(a), that further dictates the chemical pressure [Ru 2008]. With larger chemical pressure, for instance, the phase transition temperature and the energy gap scale accordingly in RETe3 systems, as shown in Figure 4.1.1(b) and (c). Comparing to the transition temperature calculated by BCS theory, which provides a fairly good prediction for CDW properties (see section 2.1.4), the CDW transition temperature shows a significant deviation. In the case of CeTe3 with a gap size of ~0.4eV, the BCS phase transition temperature calculated using (2.1.73) is 2 00 , while it is predicted to be ~500K [Ru 2006]. This lower- than-expected result can be rationalized by the fact that the Fermi surface is only partially gapped in the 51 (a) (b) (c) Figure 4.1.1 Parameters of RETe3 family. (a) Energy density at Femi level as a function of the lattice parameter of RETe3. (b) CDW gap size in various RETe3 material [Bro 2008]. (c) CDW phase transition temperature in RETe3 where heavier RE element exhibit two CDW transition temperatures [Ru 2008]. case of the CDW and thermal fluctuations inhibit CDW formation [Ru 2008]. The lattice structure of CeTe3, shown in Figure 4.1.2(a), is weakly orthorhombic with space group Cmcm, and consists of insulating corrugated double layers of CeTe sandwiched by the metallic planar nets of Te making a CeTe3 slab [Mal 2005] [DiM 1995]. The slightly orthorhombic distorted Te net is rotated 45o with respect to the CeTe double layer and has only half of the area, as shown by the structure viewed along the b-axis in Figure 4.1.2(b). The stacking of the slabs is through van der Waals gaps along the b-axis. The weak hybridization between the Te and CeTe layer causes a very large anisotropy with the ratio between the b-axis and ac-plane conductivity ≥100. From magnetic susceptibility measurements, Ru and his colleagues also indicate that the Ce is trivalent [Ru 2006]. 52 (a) (b) (c) Figure 4.1.2 Parameters of CeTe3. (a) Crystal structure of CeTe3 with the corresponding reciprocal lattice. The lattice constant 4. 4 2 .0 and 4.40 (b) The real-space model of corrugated CeTe slab (gray/red) and Te net (red) viewed along the b-axis. The coupling from px and py orbital chains from Te is also included. (c) An almost square Fermi surface calculated from a tight-binding model with extended or reduced Brillouin zone, as well as two sets of 1D bands from coupling of px and py chains. The Ce-donated electrons fill the Te p orbitals in the CeTe slab and partially fill those in the Te planes [Kik 1998] [DiM 1995]. From tight-binding modeling, there are four bands that cross Ef, which are derived from the 5px and 5py Te orbitals in the (a,c) planes, shown in Figure 4.1.2 (c) [Bro 2008]. Since these four bands form the valence band and are well isolated from others, the Te 5p orbitals define the shape of the CeTe3 Fermi surface (Figure 4.1.2(c) and 4.1.3(a)). The calculated Fermi surface correlates well with the results from APRES, shown in Figure 4.1.3(b) [Bro 2004]. Even at room temperature, the presence of a CDW can be observed, which makes the study of the CDW in CeTe3 more convenient than in other materials. CeTe3's incommensurate CDW is predominately along the c-axis of the underlying metallic planar square Te-nets at wave vector qcdw /7×2π/a where a = 4.4Å [DiM 1995]. From X-ray diffraction, the equilibrium A0 and Q0 are determined to be 0.15Å, and 0.28c*, respectively [Mal 2005]. From angle-resolved photoemission spectroscopy (ARPES), the CDW 53 (a) (b) Figure 4.1.3 Fermi surface of CeTe3. (a) Fermi surface of CeTe3, calculated from a tight-binding model, consists the coupling from px (red), py (blue), and the limits of extended or reduced Brillouin zones [Ru 2008]. (b) Fermi surface of CeTe3 measured from APRES (solid black line) [Bro 2004]. gap is determined to be 0.4eV [Bro 2004]. At the same time, from optical studies on a series of RE elements, the critical temperature (Tc) for CDW in CeTe3 to disappear is projected to reach above 500 K [Ru 2006]. 54 4.2 Experiments on CeTe3 The electron-phonon interaction that leads to various charge-ordered systems is often controversial because of the cooperative nature of the mechanism and the poor understanding of the structural aspects of the transformation. A fast, sub-ps partial recovery of electronic ordering after optical quenching has been consistently reported by earlier ultrafast spectroscopy studies [Dem 1999] [Sch 2008] [Yus 2010] [Per 2006] [Kim 2009] [Roh 2011] [Hel 2010]. This quick recovery appeared across many charge-density wave materials. This universality proved puzzling and sparked interest. One hypothesis has been that the sub-ps partial recovery may be associated with the lattice being frozen in its modulated state for a short time after optical excitation; however, there has been no direct observation. With UEC, we first investigate this long-standing puzzle on a Peierls-distored 2D CDW in CeTe3. From the CeTe3 experiment, we observe a two-step dynamics in suppression of the structural order parameter of the 2D CDW of CeTe3 that decouples from its electronic counterpart following fs optical quenching. By analyzing the Bragg reflection and its satellite peaks, we calculate the momentumdependent electron-phonon couplings of CeTe3 related to the interaction between the unidirectional CDW collective modes, lattice, and the electronic subsystem. The time scales and the relative fluctuation amplitude of these couplings allow us to determine the cooperativity between the electronic and structural subsystem in hope of improving the understanding of the mechanism of charge-ordering. 4.2.1. CeTe3 Experimental Setup and Methods The CDW of CeTe3 resides within the 2D square Te net and exhibits a uniaxial periodic lattice distortion (PLD) at wave vector Q0=0.28c*, which can be monitored by the satellite diffraction peaks to the sides of the main Bragg peaks, depicted in Figures 3.3.2(b) and 4.2.1. Following the axial assignment in Figure 4.2.1(a), the Bragg peaks are indexed as (m,n) based on the reciprocal wave vector q=ma*+nc*, while the satellites are labeled as ±Q0 next to their main peaks, Figure 4.1.1(b). Unlike 1T-TaS2, the material presented in Chapter ? of this thesis, the unidirectional p-wave CDW in 55 (a) (b) Figure 4.2.1 Experiment result on CeTe3. (a) Crystal structure of CeTe3 with the corresponding reciprocal lattice assignment with a=4.384Å, b=26.05Å, and c=4.403Å [Mal 2005]. Our femtosecond (fs) electron pulse is directed along the b-axis, producing a transmission diffraction pattern, while the fs laser pulses excite the sample area at 45 o angle. (b) The top panel shows the 3D diffraction intensity map, where the CDW satellites are located at a*± Q0 in the dashed region. The lower panels display the temporal evolution of ultrafast electron crystallography patterns subtracted by the equilibrium state pattern taken before fs laser excitation (t < 0) to showcase the induced changes. The panels show both the ps sequences for Bragg reflections and fs-to-ps sequences in a scaled-up view of the region near CDW satellites. CeTe3breaks the underlying Te square lattice and displays weak electron correlation, which presents unique advantages in deconvoluting the CDW-specific structure effects. 56 The structural dynamics are investigated by an intense 0 fs infrared = 00 nm laser pulses at 1kHz to excite electrons across the CDW gap ranging from 1 to 7 mJ/cm2 in fluence. The anisotropic electronic coupling, essential to the formation of the CDW and the quasi-1D Peierls distorted structure, is present in the asymmetric response along the c-axis. At the same time, the nonspecific phonon excitations from interaction with the hot electrons excited by laser pulses can be examined from the orthogonal Bragg peaks as comparison. Because the satellite can be two or three orders of magnitude weaker than the nearby Bragg peaks, we accumulate ~103 and ~106 electrons for the analysis of each satellite and Bragg peak in order to achieve a high signal-to-noise ratio. The change, or the dynamics, of these diffraction reflections (Figure 4.2.1(b), bottom panel) between the time before and after the 800 nm pump laser provide a clear picture of the response of our CeTe3 sample. 4.2.2 Asymmetric Character of CeTe3 First, we focus on an orthogonal pair of Bragg reflection (-4,0) and (0,4) to investigate the phononic response (Figure 4.1.2(a)) imposed on the 2D lattice by the hot carriers and CDW excitations. The change in the intensity ratio of the Bragg peak (0,4) along the CDW axis is consistently larger than the non-CDW-related one (-4,0), which indicates an elevated lattice fluctuation accompanying the melting of charge-density waves. In terms of temporal response, the phononic signatures encoded in the (-4,0) peak are delayed by ~1.5ps compared to the (0,4) one across all the fluences. This delayed response can be identified as a signature of non-CDW-related electron-phonon coupling over the 2D lattice. Furthermore, this asymmetry between the orthogonal Bragg peaks persists for more than 20 ps, indicating that the two excited phonon manifolds, one coupled to the CDW and the other generated from 2D electronic relaxations, are highly isolated from each other. The satellite peaks, which represent the CDW collective state, show a clear two-step dynamics, Figure 4.2.2(b), that is distinctively different than those from the Bragg peaks. Comparing the satellite 57 (a) (b) Figure 4.2.2 Dynamics of CeTe3. (a) The normalized Bragg peak intensity at q=-4a* and 4c* under three different laser fluences: F=2.42, 4.62, and 7.30 mJ/cm2. The error bars are based on electron counting statistics. (see Appendix A). (b) The normalized satellite intensity at qcdw=3a*+Q0 shows a nonscalable two-step suppression. response at different laser fluences (see Figure 4.2.3(a)) 80% of the maximum intensity suppression is reached within 1ps at fluence F=2.42 mJ/cm2, while it takes 3 ps to complete the same task at F=7.30 mJ/cm2. This nonscalability underscores two distinctively different processes in the satellite dynamics. The satellite peak suppression can be satisfactorily fitted by two independent exponential rise/decay channels, shown by a dashed line for the case of F=7.30 mJ/cm2 in Figure 4.2.3(a). (The fitting protocol is discussed in detail in Appendix B.) In Figure 4.2.3(a), the first channel, denoted as the fits with three different fluences is presented, and all of them exhibit 570 fs recovery time. This sub-ps time scale of , extracted from 350 fs suppression and in response to laser pulses is very similar to those reported in other ultrafast spectroscopy studies [Dem 1999] [Sch 2008] [Yus 2010] [Per 2006] [Kim 2009] [Roh 2011] [Hel 2010] [Tom 2009]. From the fitting result across a wide range of fluences, this order parameter saturates at Fc~3.8 mJ/cm2, as shown in the inset of Figure 4.2.3(b). In contrast, the slower, ps dynamics, denoted as , exhibit a fluence-dependent suppression time, as well as a linear relationship between the suppression amplitude and the applied fluence, as shown in the inset of Figure 58 (a) (b) Figure 4.2.3 Dynamics of CeTe3. (a) Detailed view of satellite intensity change at early times showing a two-step suppression, along with the two-component fits. The data from F=2.43 mJ/cm2 are multiplied by 3 in order to compare with data from F=7.30 mJ/cm2. The dashed curve shows the fitted result for F=7.30 mJ/cm2 data. The error bars are calculated based on the counting statistics. (b) The fast component of the satellite suppression , showing a fast decay and recovery. The inset shows the amplitude of the fast and slow components extracted from fitting. 4.2.3(b). This fluence-dependent ps dynamics has not been reported previously and may represent the characteristic features pertaining to the structural melting of a Peierls-distored 2D CDW. 4.2.3 Dynamics of Order Parameter of CDW in CeTe3 Due to the distinctive 1D and 2D lattice fluctuational features and the well isolated satellite dynamics of CeTe3, we can quantitatively extract the phonon and CDW dynamics using the structure factor previously derived by Guilani and Overhauser [Giu 1981]. 4.2.1 where is the reciprocal lattice vector and is the electron scattering wve vector. wave vector and the distortion amplitude of the CDW, respectively. and describe the is the Bessel function of the first kind of order n, which provides the maximum intensity of 1st order satellite (n=1) and Bragg (n=0) 59 reflections. and fluctuations ( and are the collective mode attenuation factors induced by phase and amplitude , respectively) within the CDW collective state: and 4.2.2 and 4.2. where Finally, the Debye-Waller factor is accounted by the term 4.2.4 where being the atomic lattice fluctuation. From this formulation, some observations can be made at the first glance. First, the satellites and Bragg intensities are both influenced by the CDW order parameter because for a small , and are anticorrelate with each other. Secondly, although the amplitude fluctuation plays no role in the satellite suppression ( =1), it couples strongly to soft mode near [Sch 2008] [Yus 2008] [Lav 2008] [Kus 2011] (Kohn anomaly, discussed in section 2.1.4) and directly contributes to the decay of Bragg reflection along the c-axis. Thirdly, using the symmetry related to the hot-electon-relaxation-mediated 2D lattice fluctuation, we can deduce the uniaxial fluctuations from the anisotropy ratio and, for example, in the insert of Figure 4.1.2(a). Finally, the decrease of satellite intensity can either describe the actual suppression of the order parameter term, or merely a reflection of temporal phase fluctuations term without reducing . Utilizing the distinctive feature of CeTe3 allowing us to differentiate the non-CDW-related contribution in the lattice response, we can calculate the CDW-related structural order parameter amplitude fluctuation and from our experimental results following the Giulani-Overhauser formalism, shown in Figure 4.2.4(a) and 4.2.4(b). To calculate , we have excluded the fast channel, which we attribute to a phase-related decay induced by charge melting. This exclusion yields a clean result during 1 to 4 ps, shown in Figure 4.1.4(a), showing linear increment in suppression of the order parameter 60 with Figure 4.1.4 Order parameter of CeTe3 CDW. (a) the temporal evolution of the structural order parameter . The reduction of represents symmetry recovery as described by the CDW potential evolving from double well to single well (insert). (b) The CDW collective mode fluctuational variance , deduced from anisotropy analysis. (c) CDW fluctuation amplitude order parameter correlation plot. laser fluence. The dynamical slowdown in the suppression of the structural order parameter can be understood as inherent to a second-order phase transition that is driven by the softening of lattice potential at (Kohn anomaly, discussed in section 2.1.4) [Cha 1973]. This phononic origin of the phase transition can also be observed in the corresponding increment of fluctuational amplitude parameter as the order is quenched, depicted in Figure 4.2.4(a) and 4.2.4(b). In Figure 4.2.4(c), a direct comparison between the fluctuation and the order parameter shows the CDW melting following an arc trajectory that starts from the equilibrium state with distortion fluctuation amplitude 0.15 Å [Kim 2006]. With the fact that the reaches a similar value of 0.15 Å, it suggests the initial double-well potential is quenched into a symmetric state, or the potential well literally flattened in the high-temperature CDW state, depicted in the insert in Figure 4.2.4(c). 61 The origin of the ultrafast phase fluctuation might be attributed to the reduction of the long-range coherence of the CDW collective state. Electronically induced fragmentation has been reported in nanoparticles under surface plasmon resonance excitation without significantly transferring energy into the lattice subsystem, as evidenced by a rapid nonthermal recovery in the structure factor following the electronic recovery. The presence of this electronically induced fragmentation of the CDW is further supported by the observation of topological defects in the optical reflectivity signals as the first step for the recovery of the CDW in the electronic subsystem [Yus 2010]. Another novel aspect of 2D CDW melting, not identified by optical studies, is the momentary stiffening of the lattice, which is the reason for the delay of the suppression of Bragg peak described earlier, shown in Figure 4.2.2(a). This effect can be quantified by calculating the Debye-Waller factor on (-4,0), as representative of the inherent lattice response to the fs heating of 2D electron gas. A narrowing, or decreasing, of fluctuational variance occurs nearly instantaneously, as shown in the inset of Figure 4.2.2(a). This narrowing can be translated into a stiffening in the mean atomic potential, which has been observed in graphite [Ish 2008] under similar optical quenching. The mechanism for the stiffening phenomena has been attributed to the inability of excited electrons to adiabatically follow the lattice dynamics in low-dimensional systems, modeled by a density functional theory with nonadiabatic implementation [Ish 2008]. As in graphite, this stiffening phenomenon lasts just over the hot electron lifetime (~1ps) [Sch 2008]. After that, the 2D lattice might be heated first through optical phonon emission at 0 and followed by the ensuing phonon cascades to reach thermalization, characterized by the baseline rise of , shown in the insert of Figure 4.2.2(a), on an 7 ps ( ) time scale. 4.2.4 Cooperativity Between Electronic and Structural Subsystems We have observed a sequence of events that can be traced to the interplay between the uniaxial CDW-related soft modes, the lattice phonons, and the perturbed electronic subsystem. To quantify the cooperativity, we use a phenomenological three-temperature mode (TTM) to capture the asynchronous 62 electronic and structural melting of the CDWs driven by the hot electrons and collective modes, respectively. In our TTM framework [Mur 2009], the effective local temperatures and specific heats in the electronic, CDW, and 2D lattice manifolds are labeled as and , where el, CDW, and ph, respectively. We use the coupling equations 4.2. to describe the energy exchange between these three manifolds, where is the coupling constant between two manifolds and . Because the weak out-of-plane coupling between the Te planes, the energy and charge diffusion along the z-axis can be ignored on the time scale considered here. Using the time constants (el-CDW), (el-ph), and (ph-CDW) obtained in our experiments, we can establish the constraints and solve the coupled differential equations iteratively. We also consider depth inhomogeneity in the optical excitation (laser penetration depth nm) [Sac 2007]. We find this simple three-temperature model adequately captures the key features of the space-time evolution of the thermal energy flow in and out of the CDW manifolds. A more sophisticated three-temperature model incorporating the proper z-axis diffusions and the hear capacities associated with each manifold has been published [Tao 2013]. The overall concept of TTM is illustrated Figure 4.2.5. The photoinduced CDW dynamics is initiated by the generation of hot carriers through above the CDW gap photoexcited by an intense laser pulse, . The hot carrier generated by photon quickly equilibrate with the unexcited carriers at 100 fs time scale. The optical energy stored in the electronic manifold decays into the lattice counterparts via three coupling channels: the coupling the between hot carriers and 2D lattice phonons (el-ph), the hot carriers and the CDW collective modes (el-CDW), and the 2D lattice phonons and the CDW collective modes (ph-CDW). Using time constants (el-ph), (el-CDW), and (ph-CDW) of 7 ps, 3.3 ps, 40 ps, respectively, and the formulism described above, the simulated dynamics follows well with the experimental results, depicted in the lower panel of Figure 4.2.5. In that panel, the dashed line shows the 63 Figure 4.2.5 Conceptual framework of the three-temperature model (TTM). See text for notation. TTM simulation at the surface (z = 0), while the solid line shows the simulation averaged across the sample slab from 0 to 50 nm. These simulated results agrees well with the data points, the hollow points in the Figure 4.2.5 insert. The coarse-grained through-slab dynamics observed by the transmission ultrafast electron crystallography is more than a factor of 2 less pronounced compared to the surface dynamics, which 64 provides relevant information when calculating critical fluence. suppression, as determined from the departure from linearity in The critical fluence for electronic , depicted in the insert of Figure 4.2.3(b), is reduced to 1.9 0.4 mJ/cm2, which is generally agreeing with the threshold (1-2 mJ/cm2) reported by ultrafast angle-resolved photoemission study of the isostructural TbTe3 [Sch 2008]. Using this 1.9 0.4 mJ/cm2, we obtain the critical density u.c.v u.c.v , where the reflectivity R=0.7 [Sac 2007] and u.c.v being the unit cell volume of 5×10-22 cm3 [Roh 2011]. In comparison, we also estimate the mean-field limit of the critical density based on the CDW condensation energy (Eq. 2.1.70), where the CDW gap =3.25eV, and the ungapped density of states near Fermi energy = 0.4eV [Bro 2004], the Femi energy =1.48 state/ev/(u.c.v) [Bro 2008]. The agreement between the mean-field calculated critical density, experimental-extracted = 0.8eV/(u.c.v.), and our supports the idea that the fs partial structural order parameter response is indeed correlated with the disruption of charge ordering. 4.2.5 Summary We have established a two-step structural response to the optical quenching of the CDW, in which the majority of structural suppression happens on the ps time scale, decoupled from the fs charge melting. This observation is the direct proof that the periodically modulated ionic potential well has not been significantly modified during charge melting, therefore the rapid recovery of the electronic order parameter can be facilitated as proposed by Demsar and co-workers [Tom 2009]. We think that the separation of structural and electronic order parameters is the result of the significant different in the effective mass in these two subsystems, as well as the fact that the charge ordering is inherently coupled to the valance electrons that are directly excited by the fs laser pulses. Once the electron temperature is reduced to a threshold where a stable CDW condensate can exist, the coupling between the electronic and ionic subsystems can reestablish. However, the cooling of the quasiparticle does not completely depend on the CDW, as the 2D electron-electron and electron-phonon coupling would take place in the process at 65 the quasiparticle level. Therefore, the time scales of the first channel are directly related to the quasiparticle dynamics, while it has little to do with the specific CDW mechanism. This is supported by the apparent universality of the sub-ps recovery of charge ordering from monitoring the electronic channel across a spectrum of different CDW systems. Therefore, important distinctions can be made from the ionic frame through examining the ps structural response following the electronic perturbation of the CDW. The noncooperative phononic signatures of CeTe3 illustrate a case of a fluctuation-dominated phase transition and may very well represent the nonequilibrium dynamics for an entire class of inherently Peierls-distorted electron-phonon system. 66 CHAPTER 5 Phase Transition of Charge-Density Waves Phase diagram of 1T-TaS2 is filled with unique states, including Mott insulating, incommensurate and commensurate CDW, and superconducting states. Previously these states can be accessed via thermal, chemical-doping, or external pressure treatment. Utilizing optical excitation with different energy level, we explore the energy landscape with ultrafast photo-doping to induce pathway that have never been revealed, in hope to add more knowledge to the rich content of 1T-TaS2 phase transition. In this chapter, the basic structural and charge-density waves phases of 1T-TaS2 are discussed first, then our experiment result is presented with experimental detail at the end of chapter. 67 5.1 Crystal Structure and Charge-Density Wave of 1T-TaS2 1T-TaS2 belongs to the family of layered transition-metal dichalcogenides (TMD). TMD exhibits simple crystal structures based on the stacking of three-atom thick layers, and 1T-TaS2 is the only TMD material to develop the Mott insulating ground state in a commensurate charge-density wave (C-CDW) [Sip 2008] [Faz 1979]. The middle layer of hexagonally arranged transition metal atoms is sandwiched by two planes of hexagonally packed chalcogen atoms. These three-atoms-thick layers are bonded together via van der Waals force along the c-axis, while the metallic sheets are predominately formed by covalent interaction between each Ta atom [Wil 1975]. There are two ligand coordinations can be found in TaS2: Trigonal-prismatic and trigonal-antiprismatic (distorted octahedral) coordination [Spi 1997]. While the prior case gives us the 2H-TaS2 and the octahedral structure builds the 1T-TaS2 polytype, depicted in Fig. 5.1.1(a), it is possible to observe polymorphs that consists both types [Spi 1997]. Above 1100K, the 1T-TaS2 structure can be described by the point group 3.3649 Å and 1 with lattice constants 5.8971 Å [Spi 1997]. At room temperature, the 1T form can be retained by quenching under sulphur environment if not reheated above 550 K [Wil 1975]. There are several CDW phase transitions reported on the pristine 1T-TaS2 across a wide range of temperature [Ish 1991] [Wil 1975] [Spi 1997]. At temperature below ~225K, the so called Star-of- Davis 13-atom clusters, builds up the entire C-CDW state. This polaron-like distortion is characterized by the 6 Ta atoms in each of the two rings surrounding the central 13th atom moving inwards, depicted in Fig. 5.1.1(b). This distortion couples significantly with the valance charge density redistribution within the star. When warming up across 225K, the spatial inhomogenerities start to merge by breaking up the C-CDW state into C-domains, first into a stripe phase where the CDW reconstructs into a near triclinic local ordering (T-CDW), then into a near commensurate state with hexagonally ordered domains (NCCDW) above above ~280K [Tho 1994]. Scanning microscopy determined that locally within the C- domains the CDW maintains commensuration in these textured phases, but the incommensurate regions between C-domains grows with temperature, resulting in smaller C-domains [Tho 1994]. Above 68 (a) (b) Figure 5.1.1 Structure of 1T-TaS2. (a) The tantalum atom is located at center of six octahedrally coordinated sulphur atoms. The lattice constant are 3.3649 Å and 5.8971 Å. [Spi 1997]. (b) The Star-of-David 13-atom cluster representing the unit cell of C-CDW in real space. The lattice distortion within each star is coupled with a strong charge density redistribution. The angle between the CDW vector and lattice vector is 13.9o. Tc(IC)~350K, the commensurate cells completely dissolve, and a new C-domain-free state arises with triple incommensurate CDWs (IC-CDW). Finally, the N, CDW-free, phase would set in when all the distorted Ta atoms move back to the symmetrical configuration at ~550K. A quick summary of different CDW phases in pristine 1T-TaS2 is listed in Tab. 5.1.1. The structural information of 1T-TaS2 were gained using X-ray, electron diffraction/microscopy, and scanning tunneling microscopy (STM) [Bur 1991] [Van 1992] [Rem 1993] [Tho 1994]. Comparing the results from these surface or bulk sensitive techniques, it is not surprising that the CDW formations show little difference since the quasi 2D character of the 1T-TaS2 CDW is retained by the 3D interaction. Fermi surface measurements [Cle 2007], calculations [Myr 1975], and observations of Kohn anomaly [Wil 1974] strongly suggest a classical Peierls mechanism for the IC-CDW in 1T-TaS2. However, the presence of the Mott state is still under discussion [Joh 2008] [Cle 2006] [Cle 2007]. 69 Phase C-CDW T-CDW NC-CDW IC-CDW N Temp. on cooling (K) < 183 183 < T < 347 347 < T < 543 > 543 Temp. on warming (K) < 223 223 < T < 280 280 < T < 357 357 < T < 543 > 543 Angle (o) to a* on cooling 13.9 10.9 - 12.3 0 - Angle (o) to a* on warming 13.9 13.0 - 12.3 12.3 - 11.5 0 - Table 5.1.1 The different CDW phase in 1T-TaS2 and their manifestation in reciprocal space. The values of transition temperature and angle associated with different CDW phases under the thermodynamic conditions (cooling and warming) are taken from [Spi 1997] [Ish 1991]. The exact nature of these various CDW states has been a subject of considerable debate. First, they are linked to a pseudogap (metallic) feature [Ang 2012] with polaronic conductivity [Dea 2011]. The angle-resolved photoemission (ARPES) on pristine and doped TaS2 clearly identified coexistence of a Mott-Hubbard gap and a nesting-driven CDW gap in different pockets within the Brillouin zone (Г and M-K respectively) [Ang 2012]. The most recent crystallography studies indicated that the domain walls (or solitons) are only a few atoms thick [Rit 2013], suggesting strong phase coherence between the domains. It is also an open question whether the polaronic transport is mediated through soliton regions [Sip 2008] or via a momentum-dependent mid-gap state created as part of a coherent interference effect in deconstructing the Mott C-CDW state [Ang 2012] [Rit 2013] 70 5.2 Exploration of Meta-Stability and Hidden Phases of 1T-TaS2 Phase transitions are amongst the most fascinating properties of many-particle systems, and they exhibit common features across very different scales ranging from exotic forms of nucleus [Guo 2011], structured water [Sta 2014] , to galactic evolution [Sag 2009]. Whereas classical phase-change phenomena have been well classified, exploration of phase transitions in quantum many-body systems is an emerging field. Layered transition-metal oxide and chalcogenide compounds can exhibit exotic quantum phases, including Mott insulator, superconductor, and spin or charge density wave states that competitively emerge with subtle physical tunings, such as applying heat and doping. When multiple electronic and structural orders are entangled, giant responses in the electronic and lattice degrees of freedom can occur, seen in the resistivity change by several orders of magnitude in doping (or temperature)-induced switching in manganite, magnetite, vanadium oxide, and several heavy fermion and high-temperature superconductor compounds [Ima 1998]. Identifying the origins for the competitive or cooperative emergence of various functional states responsive to doping, temperature, strain, or electrostatic and magnetic fields is of vital importance for elucidating the basic physics and their enormous technological potential. 1T-TaS2 is generally viewed as a prototype material for investigating the emergence of quantum orders in correlated electron systems [Sip 2008] because, despite of its relative simple composition, it exhibits an assortment of intriguing electronic phases, as reproduced in Fig. 5.1.2(a), including Mott insulating state, various textured charge-density wave (CDW) orders [Spi 1997], as well as recently reported superconducting phase under chemical doping [Ang 2012] [Li 2012], and pressure [Sip 2008] [Rit 2013]. Complex quantum phases emerge due to strong coupling and competition between electronic, lattice, spin, orbital and other degrees of freedom. At equilibrium disentangling of the contributions of these competing degrees of freedom is difficult; however, ultrafast pump-probe experiments can temporally isolate the various degrees of freedom unmasking hidden states that have not been accessible via conventional techniques. With UEC, we introduce high fidelity approach to revealing the ultrafast 71 (a) (b) Figure 5.2.1 Phase diagram and diffraction pattern of 1T-TaS2. (a) Generic phase diagram of 1T-TaS2 under various physical domains (temperature, doping x, or pressure P ) reconstructed based on reference [Fau 2011] [Cav 2004] [Per 2006] The CDW phase evolution can be characterized by the changes in the hexagonal CDW diffraction peaks at reciprocal vector Q: Amongst the phase transitions starting from the C-CDW, the intensity of CDW and the angle of Q (with respect to G) are reduced suddenly at the phase boundaries to approximately half and 0 (from 13.9) to the IC-CDW (upper-right corner). (b) The scaleup view of the ultrafast electron diffraction pattern, showing the hexagonal diffraction patterns of C-CDW (Q) surrounding the lattice Bragg peaks (G). structural dynamics of complex quantum materials and contributes to the recent strong interest in accessing various functional states in correlated materials using light [Sto 2014] [Fau 2011] [Ich 2011] [Jon 2013]. We utilize optical excitation to exert influence on the electronic properties, similar to chemical doping or applying pressure [Fau 2011] [Cav 2004] [Per 2006], but without uncontrolled effects due to strain or disorder. Femtosecond (fs) pump-probe method(12) offers a unique possibility to drive the system out of equilibrium by creating hot carriers while the lattice or long-range ordered states remain less perturbed initially [Han 2012]. This selective excitation creates a crucial temporal window to 72 disentangle the couplings that lead to various phase transitions. We compose a comprehensive study of optically induced phase diagrams and answer several outstanding questions concerning thermal and chemical effects induced by photo-excitation. The method of choice here is femtosecond electron crystallography, with which we address the open issue of non-thermal effects in non-equilibrium photoinduced phase transitions of 1T-TaS2. We elucidate the mechanics of coupling between macroscopic electronic and lattice-ordered states, which enable an ultrafast phase transformation occurring well within 1 picosecond (ps). Moreover, we characterize ultrafast optical doping-induced transition pathways through a succession of meta-stable phases and establish the first temperature-optical doping phase diagram to delineate the temperature and interaction-driven phase behavior of complex materials. We study the stable and transitory many-body states of 1T-TaS2 by fs optical doping using two different laser wavelengths, =800 and 2500 nm, with photon energies E of 1.55 and 0.5 eV respectively. The initial state used in the experiments is the electronic crystal situated deep inside the Mott insulating phase at 150K. Since 1T-TaS2 has an insulating gap Eg~0.3-0.4eV [Ang 2012] in this phase, the two pump energies that we used deliver distinctly different excess energy = E- Eg for driving the initial electronic temperature Te. Both pump energies produce photo-generated hot carriers that drive a quantum transition of the Mott state on the timescale of electron thermalization, as revealed in recent ultrafast spectroscopy experiments [Per 2006] [Hel 2010]. However, for the 800nm pump experiment, a phase transition into a stable metallic regime cannot be established below the fluence ~ 2 mJ/cm2, which is near the thermal threshold indicating a typical thermally driven behavior. In contrast, a pioneering ultrafast electron diffraction experiment [Eic 2010] initiated in the NC-CDW phase indicated a strong cooperativity between the CDW amplitude suppression and the electronic gap closing but without evidence of direct coupling to the domain dynamics. To be complete, we comprehensively investigate phase transitions into all of the CDW phases, studying both the temperature-driven dynamics typical of the high energy pump pulse near TC and the non-thermal behavior evidenced by the mid-infrared pump 73 pulse at low temperatures. The temperature-optical-doping phase behavior is characterized by tuning the electron temperature Te, optical doping x, and crystal base temperature TB for both pulse energies. We prepared thin flakes of TaS2 from a 1T-type bulk single crystal by the Scotch tape method widely used in exfoliating 2D materials. (See section 5.3.1 for sample preparation and section 5.3.2 for experimental details). The exfoliated, free-standing sample flakes were transferred onto a TEM grid docked inside an ultrahigh vacuum ultrafast electron diffraction chamber [Rua 2009]. For our experiments, we selected electron-transparent flakes 30-50 nm in thickness estimated by zero-loss electron energy loss spectroscopy (EELS) thickness map, as described in section 3.2. The probe electron beam density is adjusted to balance between resolution and sensitivity. For mapping the phase diagram, ~10,000 electron per pulse is used to gain efficiency, whereas for studying the dynamics ~ 500 electron per pulse is delivered to reach ~ 300 fs resolution (FWHM) at 30 keV [Rua 2009]. Our pump laser is spectrally tuned using an optical parametric amplifier, delivering 50 fs mid-to-far infrared pulses, which are expanded to 400 µm at FWHM so the selected sample flakes ≤ 0 µm wide) can be excited homogeneously. The high quality of the diffraction patterns obtained using our fs electron crystallography system can be seen in Fig. 5.2.1(b), as judged from the well separated hexagonal arrays of CDW peaks (Q) around the atomic lattice vectors (G) in reciprocal space. In the C-CDW state, the threefold-symmetric Q1(C)=1/13(3G1-G3) peak is clearly distinguished from that of the IC-CDW where Qi(IC)~0.282Gi, by the orientation angle  of the respective Q with respect to lattice G ( in C-CDW and IC-CDW is 13.9 and 0 respectively). We use the orientation angle , depicted in Fig. insert of 5.2.1(a), and the CDW-induced lattice distortion amplitude A to quantify the ordering of various textured CDW states. As well characterized in the steady state crystallography studies, described in section 5.1 and re-plotted in Fig. 5.2.2,  is temperature-dependent between TC(T) and TC(IC) and takes on sharp jumps as the phase transitions transform into soliton states (T or NC). Correspondingly A, monitored as a function of the scattering intensity at Q [ A  ICDW(Q)1/2] [Han 2012], is strongly coupled to  in thermal equilibrium, exhibiting 74 Figure 5.2.2 Transitions of 1T-TaS2 upon heating, showing complementary changes in the resistivity and the CDW orientation angle  extracted based on electron diffraction (ED) [Ish 1991]. correlated changes at the various critical temperatures. Since the 13-atom Star-of-David reconstructed in the C-CDW domains leaves only 1 electron in the uppermost reconstructed band at half-filling, it exhibits the Mott-Hubbard transition and the polaronic distortion of the C-clusters associated with filling of the lower Hubbard band (LHB). Optical doping leads to tuning away from half filling, leading to changes in phase behavior as characterized below. We studied the laser pump fluence(F)-dependent conversion of the Mott insulator C-CDW state into various phases at TB=150K. We found that at times greater than 20ps after the initial pump pulse, , shown in Fig. 5.2.3, the sample has reached a quasi-equilibrium phase, so we chose the time delays of (10ps) and (+20ps) as the reference states before and after the laser pump. The laser pump repetition rate of 1kHz corresponds to a much longer timescale. We monitored the relative change of the CDW peak intensity as well as rotational angle , and used them to map out the F-dependent phase behavior. First we describe the responses to the 800nm pump laser pulse. At fluence F=1.8mJ/cm2, Q rotates from 13.9o to 13.4o, which means the sample goes from C to T- 75 Figure 5.2.3 Typical dynamics of Bragg and satellite (CDW) peaks of 1T-TaS2. Dynamics of each components have been normalized and scaled for comparison. phase. At F=3.6mJ/cm2, Q further rotates from 13.4o to 12.9o, going from T to NC-phase. Between F=3.6mJ/cm2 and F=6.0mJ/cm2, it is in the NC* state (see discussion below) and above F=6mJ/cm2, IC state is the final state. Intriguingly, this 1.8 mJ/cm2 threshold for entering the T-phase, evidenced by CDW gap reducing to the NC level and the formation of a mid-gap feature, is also found to be the threshold for melting the Mott state in the latest ultrafast photoemission study [Hel 2010]. Below this threshold, the quenching (partial) of the Mott gap is still clearly visible although the effect is reversed within 680 fs [Per 2006], suggesting the existence of a structure-bottleneck for stabilizing the new phase. At this threshold, the electronic temperature reaches 3000 K initially [Hel 2010]. For the 800nm pump pulse, a calculation of the energy transferred to the lattice in the final state indicates the transitions above 76 Figure 5.2.4 Comparison between the thermal and optically induced changes of over absorbed energy density (see section 5.3.4 for calculation). The temperature of 1T-TaS2 is at 150K initially. are consistent with the transition temperatures found by conventional means, confirming that at this pump energy the behavior can be described using thermodynamic reasoning. However for 2500nm wavelength pump we find that the optically driven phase transitions in 1TTaS2 are nonthermal. To demonstrate this, we map out the fluence-dependent phase behavior for the midinfrared pulse and compare it to the phase behavior described above for the 800nm pump. To make this comparison, we convert fluence-dependent maps at the two wavelengths into absorbed energy-density maps, seen in Fig. 5.2.4, which clearly shows that the critical energy densities for inducing various quasiequilibrium phases are very different for the two laser energies. In Fig. 5.2.4, the black curve is the reference curve of equilibrium measurement shown in Fig. 5.2.2 in red solid dots, but only the horizontal axis is converted into absorbed enthalpy (H) based on integration of specific heat (see section 5.3.4 for calculation). This result shows that energy density required for phase transition with 800nm photons is slightly higher than the thermodynamic value, while that with 2500nm photons is much lower. 77 Figure 5.2.5 The optically induced evolution of CDW states characterized by CDW suppression (in ratio, based on unperturbed CDW intensity) and orientation angle at various absorbed photon density for two different pumps: 800 and 2500 nm. To understand the effects of photo-doping, we convert the enthalpy change into carrier density , assuming that each absorbed photon generates an electron and a hole). Using photodoping as the axis, the two curves for the 800nm and 2500nm pump pulses now agree very well, seen in Fig. 5.2.5 as black points. The result shows that to induce the same state with different wavelength pumps, it is necessary to induce the same density of charge carriers rather than to provide the same enthalpy change. This strongly suggests that the system is driven by charge carrier doping, rather than through thermal pathways. Moreover, photo-doping has similar effects as those produced via chemical or electrostatic doping, as the optical doping effect relies on electron/hole asymmetry, common in TMD and 78 many other correlated electron crystals [Ima 1998]. Upon pumping electrons into the conduction band, a spontaneous charge separation occurs due to the more restricted dynamics of the holes left in the LHB, effectively shifting the chemical potential, hence the coupling near EF, thus creating a transient doping effect [Sto 2014] [Per 2006] [Dea 2011]. We show here that while the typical electron-hole recombination timescale is on the ps timescale at low doping, once a new metastable state is transiently entered, the energetics of the interaction potential change fundamentally, leading to a lock-in to a new charge density and a stability that is beyond the first 100 ps [Sto 2014]. We now compare the critical optical doping level to the doping carrier-density induced by applying electrostatic fields or chemical doping in other TMD materials, which commonly develop CDW states at or close to half-filling. A large capacitance sustained by an ionic liquid electrical double layer (EDL) has been used to deliver a 2D carrier density n2D up to 1.5×1014 cm-2 by electrostatic doping to vary the band filling in MoS2 [Ye 2012], and a field-doping-induced superconducting (SC) dome was established with a peak at n2D = 1.5×1014 cm-2. Optical doping in 1T-TaS2 can easily reach this level, and the n2D calculated from the critical doping at the C-to-T and NC-to-NC* boundaries are 0.5×1014 and 1.3×1014 cm-2 respectively, matching the critical values found in MoS2 very well. The corresponding doping level is x=0.05 and 0.12, which is often sufficient to induce new phases by chemical doping. To our knowledge no one has been able to gate-dope 1T-TaS2 with EDL because of its high intrinsic carrier concentrations. The optical doping method established here offers an alternative route to access higher doping concentrations than chemical doping, and to explore various doping-induced novel quantum many-body states without substantially deforming the lattice. We have explored the experimental analysis of photo-doping-induced phases in various temperature regimes from which we extract a first temperature-carrier density phase diagram for 1T-TaS2 as depicted in Fig. 5.2.6. Comparing to Fig 5.2.6 and Fig 5.2.1(a), the temperature-photo-doping phase diagram is strikingly similar to that found for the generic chemical doping (or pressure) phase diagram presented. At low T the critical density (or pressure) is insensitive to the temperature changes of the 79 Figure 5.2.6 The temperature – photon-density phase diagram of 1T-TaS2. sample, and the phase transitions may be characterized as interaction-driven where new dominant phases emerge from the change in the free energy of different states resulting from chemical potential shift. Conversely, in the regime with low doping (or pressure), the phase transition is mostly temperature-driven. Based on this phase diagram, the thermal-like emergence of metallic state investigated using the 800 nm pump in the previous ultrafast photoemission studies of 1T-TaS2 [Per 2006] [Hel 2010] is expected as the experiment was conducted in the temperature-driven region near TC(T) and limited to the boundary of insulator-metal transition. Similar conclusions have been drawn from studies of other correlated electronic crystals[Jon 2013] [Bau 2007], which are expected to have similar generic forms in their phase 80 Figure 5.2.7 The dynamics of CDW state transformations inspected via the rotation of CDW wave vector Q away from C-CDW and the suppression of ICDW(t) [in ratio based on the ICDW(-10 ps)]. The solid lines are drawn based on fitting the stair-case rises using a Gauss Error function. diagram. Limited by our current cooling capability ≥ 20K) , we were unable to inspect the emergence of SC (TC = 8K at optimal doping) within the T and NC states. However, we discover that a hidden state not observed in the thermodynamic phase diagram, termed here as the NC* state. As indicated in Fig. 5.2.5, the NC* can be characterized as a precursor to the domain proliferation in the NC-to-IC transition, or a self-organized subdivision of domains before complete dissolution of commensurate cells. The intermediate domain structure between the NC and IC states is meta-stable in the dynamical regime, 81 evidenced in the continuous transition, Fig. 5.2.5, but absent at the thermodynamic timescales of the transition from NC to IC state, Fig 5.2.2. A remarkable capability of the ultrafast crystallography data is to study the nonequilibrium transition state pathways evident in Fig. 5.2.7. The dynamical transformations are explored using 2500 nm photons and TB=150K, in a region predominantly driven by doping effects. We drive the system with three selected photon densities, targeting the ‘final states’ of T, NC, and NC*. This near-gap mid-infrared pump ensures a small excess energy or thermal imprint on the dynamics after reaching the quasiequilibrium state. The results of satellite peaks dynamics are depicted in Fig. 5.2.7, where the upper panel shows the evolution in , and the lower panel depicts the corresponding changes in A (through the ICDW). Intriguingly these transient features are highly organized and exhibit unexpected sharp jumps in temporal steps as short as 200 fs (2 in error function fit, resolution limited). All of these sharp transitions are followed by a plateau region, defining the characteristic values and , which can be traced to the quasi-equilibrium phase map depicted in Fig. 5.2.5. for the various CDW states; however the emergences of these two order parameters are not synchronized. Quite persistently, the shift of CDW amplitude leads the change of angle in time, implying suppression of the local charge density amplitude within the C-CDW domains is a precursor for setting off the domain dynamics and deconstruction (as described in Fig. 5.2.8). Moreover the emergence of a higher-doped phase cannot proceed without the lower-doped one being established first, leading to a succession of steps in the dynamics. The only exception may be for the occurrence of T, whose domain structure is not substantiated and the first clear jump following the pump is the NC structure (Fig. 5.2.7, upper panel), whereas according the amplitude suppression (Fig. 5.2.8, lower panel) a well-defined shift into that characteristic amplitude similar to the quasi-equilibrium T state can still be identified. It is important to note that these transformations occur largely within the typical electron-lattice coupling time of the system (several ps), so the evolution may be considered to be within a closed system with essentially no change in temperature. Furthermore, in contrast to the quasi-equilibrium map (Fig. 5.2.5.) the emergence of the NC* state at 82 is very Figure 5.2.8 Cartoon depiction of the dynamical evolution CDW states in a zig-zag pathway over the free energy contour defined by the changes in and A2 based on the dynamics extracted from (A). A is scaled to 0.15Å at C-CDW state based on reference [Spi 1997]. distinct and leads to another sharp jump into the quasi-IC state (IC* in Figs. 5.2.7 and 5.2.8.), which is meta-stable at nearly continuous all the way to canonical IC state ( 13.9°) depending on the strength of excitation. All the transformations cease to evolve after 4ps, which we assign as the timescale for carrier recombination [Sto 2014]. The observed phase conversions, namely the presence of a threshold and an incubation period inversely proportional to the pump flux, indicates that the phenomena we described are in the class of photoinduced phase transitions (PIPT) [Nas 2004]. A simplified 1D PIPT model introduces a long-range coupling term in an equation of state to treat a photo-doping-controlled inter-conversion rate describing the transition between two states with these major features [Oga 2000]. However, to capture the firstorder-like sharp transitions in many PIPT systems, e.g. manganites [Ich 2011]] [Tak 2005] and organometallic spin-crossover complexes [Oga 2000] [Lor 2009], one would require a 2D simulation 83 treating inhomogeneous spatial variations seeded by photo-excitations [Nas 2004] [Oga 2000]. Such a percolative pathway necessarily engenders time-consuming steps with difficulty in accounting for the observed femtosecond scale switching, given the typical NC domain size of 73 Å [Tho 1994] and the large size of the crystal. We speculate that PIPT might be better described by a highly self-organized, nondiffusive process involving collective polaronic waves or mesoscopic quantum correlations to access different topologically distinct states in the femtosecond timescale, as seen in Fig. 5.2.8. However more theoretical analysis and experiment is required. We expect this 1T-TaS2 study will have significant ramifications in several areas of research. First, the presented methodology opens up a new avenue to survey the complex energy landscape and provides a new perspective on doping-induced phase diagrams, avoiding the difficulty of electrostatic gating or confounding effects due to defects and/or disorder when doping by intercalation or substitution. Second, the speed and degree of photodoping substantially exceeds that achievable by the conventional methods, creating the opportunities to generate new phases, as evidenced in recent studies [Sto 2014] [Ich 2011]. Third, observation of robust non-thermal switching at meso-scales and at ultrafast times provides a platform for new applications of correlated crystals for designing high-speed low-energy consumption nano-photonics and electronics devices. I would like to thank for the time and sweat Faran Zhou spent on this 1T-TaS2 phase diagram project. Without his delicate hands in sample preparation, his experimental skill in instrumentation, and his persistent work in data analysis, this project would not exist. 84 5.3 Additional Materials for 1T-TaS2 experiment 5.3.1. Sample Preparation The high quality single crystal 1T-TaS2 are synthesized by our collaborator Dr. Christos Malliakas in Prof. Kanatzidis' group at Northwestern University. The method of synthesis is described by Chris in the following paragraph. Single crystals of 1T form of TaS2 were grown by the chemical vapor transport technique. Pure elements of Ta (1.426 g) and S (0.518 g) were loaded with a 1:2.05 ratio into a fused silica tube (9 mm in diameter and around 24 cm in length) together with a small amount of I2 (0.068 g). The tube was flame sealed under vacuum (< 10-4 torr) and placed in a dual zone furnace with a hot zone at 950 ºC and a cold zone at 900 ºC. The temperature was ramped up in 1 day and the tube was soaked for 2 days at the target temperature. After 1 day of cooling time, single crystals of different sizes were formed on the cold side of the tube [End 2000]. After receiving the 1T-TaS2 bulk material, which was sealed in ~10-3 torr vacuum to minimize oxidation, we cut a thin piece from the bulk sample with razor blade to obtain the initial piece, pictured in Fig. 5.3.1(a), for mechanical peeling [Nov 2005]. The initial piece of 1T-TaS2 is sandwiched between two scotch tape or wafer dicing tape, then cleaved when the two tapes are peeled apart. Since 1T-TaS2 is a 2D material, this exfoliating technique yields flat surface cleaved along the lattice plane, shown in Fig. 5.3.1.(b). With multiple times of cleaving using scotch tape, the 1T-TaS2 can be thinned down to below 30nm in thickness. The samples can be prescreened in thickness by monitoring the transparency under optical microscope with light going through the sample stage, shown in Fig. 5.3.1 (c) and (d). The sample thickness can be measured by AFM once the material is transferred to silicon surface or by EELS function of a TEM, described in section 3.2, if the sample is transferred to a TEM grid. To transfer those 1T-TaS2 pieces on tape onto a silicon surface, we put a drop of acetone on the cleaned silicon chip, then cover the silicon with the scotch tape while 1T-TaS2 samples facing the 85 (a) (b) (c) (d) Figure 5.3.1 Optical images of 1T-TaS2. (a) Optical picture of cleaved 1T-TaS2 from bulk as a starting piece for exfoliating. (b) 1T-TaS2 on scotch tape after exfoliated once. (c) Optical image of peeled 1TTaS2 sample taken with light coming from below the sample stage. (d) 1T-TaS2 samples after multiple "peeling". silicon. The tape is pressed against the silicon by hand for several minutes to ensure high transfer rate. The acetone would dissolve the glue on tape and release the 1T-TaS2 pieces from tape to silicon, shown in Figure 5.3.2 (a). The samples on silicon are perfect for thickness measurement, as well as the electrical measurement in the future if implemented. To transfer those 1T-TaS2 pieces from scotch tape to TEM grid, we first suspend the 1T-TaS2 in acetone by sonicating the scotch tape in acetone for a few minutes. Then the acetone solution is dropped onto a TEM grid and the 1T-TaS2 would be suspended on the grid after acetone is dried up, shown in Fig. 5.3.2(b). The thickness of sample on a TEM grid is measured based on the EELS thickness map method, 86 (a) (b) Figure 5.3.2 Optical images of 1T-TaS2 samples. (a) Thin 1T-TaS2 samples on silicon surface. (b) 1TTaS2 samples on TEM grid ready for UEC experiment. described in section 3.2. 5.3.2. Experimental Details To study the phase transition of 1T-TaS2, our sample cryogenic sample holder is upgraded to achieve low vibration while maintaining low temperature capability. By suspending the cryogenic motor that creates vibration when cycling the helium into the cooling column with an aluminum frame secured to walls and floor, we isolate the sample column from the motor and minimize the vibration transmitting to the sample holder. We are able to minimize the vibration level below 5um or our detection limit while 87 maintaining the cooling capability of 20 K. The sample holder temperature is measured with 0.01K precision. The TEM grid containing 1T-TaS2 for experiment is clamped into a cooper countersink on the sample holder. The sample temperature is calibrated to be within < 1K of the measured reading using the phase transition temperature of VO2 [Tao 2012]. The UEC pump-probe setup is identical as those used for CeTe3 experiment, described in section 3.3, except the addition of 2500nm laser as optical excitation. The 2500nm laser is generated by TOPAS from Spectral Physics (described in section 6.3), driven by a 45 fs, 800nm amplified laser system (Spectra Physics, Ti: Sapphire, Regenerative Amplification). In the 1T-TaS2 experiment, the size of pump beam of different wavelength is adjusted by varying the position of a focusing lens in the path, and is characterized by the knife-edge method in situ. The pump size is set at ~400um in FWHM, which is more than 10 times larger than the 1T-TaS2 sample size to ensure the homogeneous laser fluence across the sample. For the dynamics of CDW state transformation, we use the ~500 e- per pulse as electron probe, which is estimated of pulse-length of 300fs in FWHM that defines the shortest response time in our experiment [Tao 2012]. 5.3.3 Data Analysis for 1T-TaS2 Experiment We focus the data analysis on determining the satellite peak intensity and the orientation angle between the CDW wave-vector (Q) and the lattice vector (G) (see Fig. 5.3.3). To obtain the satellite peak profile, we employ line intensity scans along the direction perpendicular to CDW vector crossing the CDW peaks. The width of the line scan is set as twice of the FWHM of the CDW peaks so it covers most of the individual peak but not the neighboring peaks. To determine the peak location and intensity, we use Gaussian function to fir the peaks with second order polynomial background underneath the Gaussians. Same fitting methods is also used for Bragg peak analysis. The angle the Q and G vectors are calculated. 88 is determined after (a) (c) (b) (d) Q G (e) Fig. 5.3.3 Diffraction pattern of 1T-TaS2. (a) Diffraction pattern of 1T-TaS2 in the NC-CDW state taken at room temperature. The image is in logarithmic scale to make CDW peaks more visible. (b) Scale-up view of the diffraction pattern from the square region in (a), showing clear hexagonally distributed firstorder CDW satellite peaks around the central lattice Bragg peaks. Second-order CDW satellite peaks are also visible. (c-e) Time-dependent diffraction images from a single Bragg peak region at different time delays: -1ps, +1ps, +3ps respectively. The solid line connects neighboring Bragg peaks, representing the direction of the lattice vector G. The dashed line connects neighboring CDW peaks, representing the direction of the CDW vector Q. ϕ represents the angle between CDW and Bragg vectors. In (e), CDW vector rotates fully into the lattice vector direction, indicating that the NC-CDW is transformed to ICCDW by 3 ps. 5.3.4. Calculation of Energy and Photon Density We determine the absorbed energy density using the following formula: . .1 89 Figure 5.3.4 The determination of CDW phase boundaries based on presence of a step or a slope change. where is the pump fluence on sample surface, R is the reflectivity and is the penetration depth of each wavelength laser calculated from the optical constant measurements in literature [Bea 1975], and is the sample thickness. From the literature, the reflectivity for 800nm of 1T-TaS2 is 0.45 while it is 0.58 in the case of 2500nm laser. The penetration depth is calculated to be 30nm for the 800nm at both room temperature and 150K. Given the phase diagram is determined at a longer time, +20ps), at which the carrier density is expected to equilibrate between different layers over the range of t, we use the thickness t as the denominator in Eqn. 5.3.1. Since for 2500nm laser, however, the calculated penetration depth is 100nm 90 at room temperature and 130nm at 150K, which are significantly larger than the 40nm sample thickness, we use in the denominator in Eqn 5.3.1. For calculating the energy density absorbed by the sample required to induce thermodynamic phase transition from our base temperature, 150K, we integrate the hear capacity and latent heat of 1T-TaS2 in the temperature range we work with. Based on the reference [Suz 1985], we calculate the energy density needed to induce thermodynamics phase change using . .2 5.3.5 Constructing Phase Diagram The temperature-photon-density phase diagram, Fig. 5.2.6, is constructed based on the critical density of the emergence of each CDW state via monitoring the CDW wave vector Q and the intensity I(Q). The absorbed photon density is converted from absorbed energy density, Eqn. 5.3.1., via . . where is the photon energy. We characterize the boundary between different phases by a step in the angle ϕ of Q relative to G, or by the slope change of ϕ 5.3.4. 91 , as exemplified as those blue circles in Fig. CHAPTER 6 Dynamics of Nanoscale Water on Surface The property of water has been great interests to scientists due to its ubiquitousness in our lives. The prospect of elucidating some mystery on the most intriguing molecule is a dream project for many. However, studying the property of water inside an ultra-high vacuum chamber that also houses a high voltage electron gun, a highly sensitive mass spectrometer, and several ion gauges adds more challenges to the task. In reality, all these expectation or difficulties only make the project more irresistible. In this chapter, we first introduce the long-time curiosity on water, and then present the modification and enhancement implemented for this water experiment. Finally we discuss the result and prospect of the project. 92 6.1 Structure and Dynamics of water Water is often perceived as ordinary since it is ubiquitous in the world. It is composed by two common reactive elements, two hydrogen atoms attached to a single oxygen atom. It can act as a solvent, a solute, a reactant, and a biomolecule that provides structure for proteins, nucleic acids, and cells. Despite its simplicity in composition and small size, it is the most extraordinary substance as the existence of life on Earth depends on its special properties that nurture everything we know. Simply put, life would not exist without the presence of water. Despite water being the second most common molecule in the Universe, right behind hydrogen, many of its properties are not well understood. When comparing to the hydrides of neighboring element near oxygen, the water boiling point is out of the trend. Following the trend from the periodic table, water should be in a gaseous form at 1atm. In its liquid form, it does not behave like other liquid either. Its density reaches a maximum at 4 oC in liquid form, which is not typical. Often liquids have higher density in the solid phase. The compressibility of water is minimized at 46.5C as other liquids usually get more compressible when heated up. Its viscosity decreases as higher pressure is applied, which is in the opposite trend of other liquids. Under pressure, the melting point and maximum density point of water shift to lower pressure, which is again at odds with other liquids. Since Rontgen, 1901 Nobel Laureate, suggested a mixture of ice dissolved in monometic water in 1891 [Ron 1892], the study of state and phase transition of water has sparked much interests and debate. In his “Structure of Liquid Water” paper, Rontgen believed the anomalous properties of water can be explained if we assume that “liquid water consists of two types of molecules with different structures. Molecules of the first type, which we would like to call ice molecules since we are going to ascribe to them some properties of ice, undergo transformation into molecules of the second type when the temperature is increased. Thus, we consider water at any temperature as a saturated solution of ice molecules whose concentration is higher when the temperature is lower.” His paper described for the first 93 (a) (b) Figure 6.1.1 Purposed structure of water (a) LDL and (b) HDL [Cha 1999]. time what is known as the two-structure model of water. In the subsequent hundred years to come, his two-state postulate has evolved into an equilibrium between two types of structures, often called lowdensity liquid (LDL) and high-density liquid (HDL). It is believed that these structures LDL and HDL form hydrogen-bonded network with localized structure and clustering, illustrated as Figure 6.1.1(a) and (b), respectively. . Numerous experiments have tried to observe the existence of two-state water. Huang and colleagues [Hua 2011] used X-ray to study water structure at different temperatures. The intermolecular pair-correlation function (PCF) g(r), shown in Fig. 6.1.2, shows an increment in intensity at 3.3Å, which correlated to high-density water clusters with increasing temperature. At the same time, they also observed a diminishing intensity of the dome at r=4.5Å that corresponds to the O-O distance that does not occur in the dense ice form with increasing sample temperature. Both of these phenomena points to a transformation or transition of LDL into HDL, however, the result is not conclusive due to possible truncation or background subtraction during their data analysis. In 2003, Wang and his colleagues studied the spectral diffusion in the OH stretching band of 94 (a) (b) (c) Figure 6.1.2 Optical studies on water (a) comparison of g(r) of liquid water measured at 7, 25, and 66 oC with X-ray. (b) Raman spectra with 3115 cm-1 pumping, fit using the two Gaussian sub-bands V(red) and V(blue). (c) Time dependence of red and blue band with 3115 cm-1 pumping at different temperature. water, the transition, using ultrafast IR-Raman spectroscopy. The Raman spectra, shown in Fig. 6.1.2., exhibits ps dynamics at two peaks, marked as red and blue, associated with O-H bond stretching in water. However, like many Raman spectroscopy result, the fitting of the spectra and assignment of the bands can be controversial, and it lacks the direct observation of lattice structure. With the molecular beam doser that deposits water onto the sample surface in our ultra-high vacuum chamber[Mur 2009], a low-vibration cryogenic sample holder that goes down to 20K, and 95 ultrafast electron crystallography with wavelength-tunable excitation laser, we are poised to study the structural dynamics when water sublimates at low temperature. 96 6.2 Experiment Setup The UEC experiment setup for ice/water observation, shown in Fig. 6.2.1, is very similar to that used for CDW material, described in section 3.3, except for the usage of the molecular beam doser and the 3000nm laser utilized for hydrogen-bond excitation. The ultrafast pump-probe is driven by a Ti:Sapphire femtosecond laser system that delivers 2.5mJ/cm2, 50fs, 800nm laser pulses at a 1kHz repetition rate. The output pulses are split into two paths, pump and probe, by a beam splitter. The laser pulses along the pump path drive an optical parametric amplifier (OPA) that generates a board range of selectable optical wavelength, from 285 to 2700 nm. The laser output from this OPA is further combined to generate the 3000 nm laser that is in tune with the vibration mode of hydrogen bond in water. The method of generating this mid-infrared is detailed in section 6.3. The laser pulses along the probe path are frequency-tripled into ultraviolet pulses (266nm, 4.7eV) that drive the fs photoemission from a Ag photocathode to form the probe electron beam. The photoelectrons are consequently accelerated to 20-40 keV and focused by a short-focal distance magnetic lens into a 5-30 µm narrow probe to interrogate the nanoscale water layer by the way of electron diffraction [Rua 2007]. The ultrafast electron diffraction technique for the water experiment is identical to that used in CDW materials, described in section 3.3. The diffraction pattern from ice/water resembles the powder diffraction type from randomly oriented water crystals formed on substrate. In the reflective diffraction geometry, shown in Fig. 6.2.2(a), the electron "bounces" off the ice/water layer on silicon and diffracts to the CCD camera. The main advantage of the reflective diffraction is the ability to interrogate a larger sample area thanks to the small incident angle, typically 0.5 to 5o. However, in this geometry, due to the existence of a supporting substrate, the diffraction cone is cut into half by the shadow edge, equivalently losing half of the 97 (a) (b) (c) Figure 6.2.1 Experiment setup. (a) Experiment setup for ice/water related experiment. Different diffraction geometry and corresponding water diffraction image obtained on CCD camera in reflection diffraction setup and (b) transmission diffraction setup. experimental signal. Additionally, due to this larger footprint of probed area, the arrival time of the pump laser would be slightly different within the sampling area, which increases the time resolution in the experiment. On the other hand, in the transmission geometry shown in Fig. 6.2.2(b), the electron penetrates through the sample and substrate to form the diffraction image on our CCD camera. The time resolution is minimized because of the small size of the sample area, equivalent to the size of the electron probe. However, the experimental signal is also reduced because less ice/water crystal is sampled. The ice/water layer on substrate is delivered via our molecular beam doser built by Dr. Ryan Murdick [Mur 2009]. The water is injected onto the substrate surface at 90 K in an ultra-high vacuum 98 environment, and ice crystals are formed within a few hours after the water dosing. More detail regarding the ice/water layer formation can be found in section 6.4. I would like to thank Peter Lee for designing the cryogenic sample holder that made this project possible. Peter's innovative design on the sample holder enabled us to conduct experiment at T = 14K while maintaining the pump/probe access to the sample and the 4-axial freedom of sample movement. 99 6.3 Generation of Mid-IR Excitation Laser via Nonlinear Optics One of the most direct methods to study the dynamics of the water network is to excite the OH stretching vibrations [Cow 2005] [McG 2006], which are strongly coupled with the Hydrogen bonding that is associated with the distribution of hydrogen-bonded structures and the intermolecular forces that dictate the structural dynamics of the liquid [Fra 1972]. In simplest term, the vibration modes of OH bond in water can be mainly characterized by the symmetric stretch stretch , bending , and asymmetric modes, illustrated in Fig. 6.3.1(a). The frequency associated with these modes ranges from 3210 to 3755 cm-1 for and , and 1595 to 1670 cm-1 for the mode across a wide range of temperature, summarized in Table 6.3.1 [For 1968]. However, our OPA can only output laser light with frequency > 3700 cm-1, or < 2700 nm in wavelength. Therefore, we have to generate the ~3000 nm midinfrared by building additional nonlinear interaction using the available output provided by OPA to excite OH stretching modes. Long before the invention of the laser, the nonlinear-optical effects have been observed in, for example, Pockels and Kerr electro-optic effect [Boy 2003] and light-induced resonant absorption saturation, described by Vavilov [Val 1950]. However, the optical nonlinearities only broadened its catalog after the advent of lasers that provided the much needed intensive energy for such a phenomena. In 1961, Franken et al. [Fra 1961] first observed the nonlinear optical effects, the second harmonic generation (SHG), in the laser era. During next year, 1962, Terhune et al. first reported the observation of third harmonic generation. Then in the next four decades, the field of nonlinear optics has experienced an enormous growth, leading to the observation of new physical phenomena and giving rise to novel concepts and applications. The nonlinear-optical concept can be found in many excellent textbooks by [She 1984], [Boy 2003], [Cor 1990], and [Rei 1984]. Nonlinear optical phenomena occurs when the response of a material systems to an applied field depends in a nonlinear manner on the strength of the optical field. The induced dipole moment per unit volume, or polarization , of a material depends on the strength of 100 of an applied external optical (a) (b) (3058 nm) (3082 nm) (3096 nm) (3115 nm) (2967 nm) (2990 nm) (3003 nm) (3021 nm) Figure 6.3.1 OH vibration modes of water. (a) Illustration of three vibration modes in OH bond of water. (b) Experimental observed frequency for OH vibrations in water [For 1968]. The corresponding wavelength for some frequency is listed in red. field. In the case of conventional, or linear, optics, the induced polarization depends linearly on the electric field strength that can be described by . .1 where is known as the linear susceptibility and is the permittivity of free space. In nonlinear optics, the optical response can often be described by a more generalized Eqn. 6.3.1 by expressing the polarization as a power series in the field strength as . .2 The and are known as the second- and third-order nonlinear optical susceptibilities, respectively. When we treat the fields in a vector nature, then becomes a second-rank tensor, 101 becomes a third rank tensor, and so on. Here we have assumed the polarization at time t depends only on the instantaneous value of the electric field strength, and the medium must be lossless and dispersionless. At the same time, the and are referred to as the second- and third- order nonlinear polarization. In general, the second-order nonlinear optical interactions can occur only in non-centrosymmetric crystals, namely crystals that do not display inversion symmetry. On the other hand, third order nonlinear optical interactions can occur for centro- and noncentrosymmetric media. When we represent the electric field in the form of a sum of two monochormatic waves, or . . the second-order nonlinear polarization of a noncentrosymmetric material can be written as . .4 Eqn. (6.3.4) can also be expressed in . . We can express the complex amplitudes of the various frequency components of the nonlinear polarization as second harmonic generation SHG , second harmonic generation SHG sum frequency generation SFG difference frequency generation DFG optical rectification R . . The process of SFG, which is illustrated in Fig. 6.3.2(a) and (b). The process of SHG is just a special case of SFG with which is useful to produce radiation in the ultraviolet spectral region. On the other hand, DFG, illustrated in Fig. 6.3.2(c) and (d), can be used to produce infrared radiation. By following the energy conservation in the interaction, we can relate the wavelength of each wave in SFG or DFG using 102 (a) (b) (c) (d) Figure 6.3.2 Different nonlinear process. (a) Geometry of sum-frequency generation. (b) Energy-level description of SFG. (c) Geometry of difference-frequency generation. (d) Energy-level description of DFG [Boy 2003]. for SFG or for DFG . .7 One can readily control energy of the output laser by choosing the appropriate energy level of input waves. Typically the three waves involved in SFG and DFG interactions are named as pump, signal, and idler according to their respective wavelength, . .9 103 In Eqn. 6.3.6, there are four nonzero frequency components and all those these four are present in the nonlinear polarization. However, typically one of these frequency components will be dominate in the intensity. It is because the nonlinear polarization can be efficiently produced if a certain phasematching condition is satisfied, and usually this condition cannot be satisfied for more than one frequency component. Practically, one can choose the desired frequency component by adjusting the polarization of each waves by the phase-matching condition, . . via orientation of the input waves By examining the availability of our TOPAS output wavelength, it is the most direct to utilize 1256 nm and 2165 nm lasers from TOPAS to generate 2991 nm, which is chosen to directly excite the OH vibration modes and of ice at low temperature, as listed in the Fig. 6.3.1, through the DFG interaction, Eqn. 6.3.7, 1 12 1 1 = 21 2991 . .10 The optics setup to generate the ~3000 nm laser beam for the OH vibration in water is illustrated in Fig. 6.3.3. In Figure 6.3.3, our OPA is driven by a Ti:Sapphire femtosecond laser system with 1.0 mJ/cm2, ~50fs, 800 nm pulses at 1kHz repetition rate. Using this source, OPA can be adjusted to output a 1256 nm signal beam at ~200 µJ/cm2 (shown in green color in Fig. 6.3.3) and 2165 nm idler beam at ~97 µJ/cm2 (shown in red) in order to generate the 3000 nm laser at the nonlinear crystal AgGaS 2 (part number AGS-401H from Altos photonics). We use the 1st delay stage in the 2165 nm laser path to optimize the temporal overlap of two input lasers. At the same time, a dichroic mirror (DM), which allows 2165 nm to pass through while reflects 1256nm laser, is placed in the path of both so they can be directed to the AgGaS2 crystal for DFG interaction. Since all three lasers involved here are not visible, the optimization of the alignment can be tedious. A step-by-step procedure is listed below as reference: 104 Figure 6.3.3 Optics path and setup for mid-IR generation. The green line indicates the 1256 nm optical path. Red line represents the 2165 nm laser path. The blue path is where the 3000 mid-IR travels. The M1 to M7 mirrors are purchased for the high reflection on 1256 nm and 2165 nm, while M8-M12 are Au coated exhibiting low loss for the infrared range. The purple arrows indicate the polarization of each wave. 1. Optimize output power from TOPAS. To optimize TOPAS output, one should minimize the pulse temporal width of 800nm. This can be roughly achieved by optimizing the 266 nm output from our tripler. 2. Roughly match the optical path length of signal and idler, so the temporal overlap of both lasers on the nonlinear crystal is not far off. 3. Place the nonlinear AgGaS2 crystal with 5 deg tilt from vertical [(phase matching angle ~ 44o) (cutting angle ~39o)] 4. Make spatial overlap between signal and idler on the AgGaS2 crystal. 105 a. Place a long-pass filter right after DM to minimize those visible lasers below 1000nm that may interfere the visual inspection of those invisibles. b. One can visualize the location of the signal, idler, and 3000 lasers on a thermochromic liquid crystal sheets that would changes color with heated by the incident lasers. 5. With temporal overlap (adjusting 1st delay stage) and spatial overlap (adjusting 2 mirrors right before DM and DM) both close to optimal, try to locate a 800nm laser between the signal and idler after the nonlinear crystal. This 800 nm is generated by SFG from the signal and idler since all components in Eqn. 6.3.6 do occur in the nonlinear process. Since SFG is more efficient than DFG, this 800 nm is much easier to locate, and can be used as an indicator for optimizing the temporal and spatial overlap. 6. Once the 800 nm from SFG is close to optimal, one should be able to locate the mid-IR 3000 nm near the signal spot using a thermochromic liquid crystal sheet. 7. Remove the long-pass filter. Optimize the 3000nm power by adjusting the delay stage, mirrors, and tile angle of AgGaS2 crystal. The maximum power of the 3000 nm beam we can achieve is 13 µJ/cm2, that represents a conversion efficiency of 6.5% ( the power of 3000nm / the power of 1256nm signal ) which is on par with that obtained by Prof. McGuire (7.0%) who taught us invaluable knowledge when he guided us through the alignment process at the inception of our mid-IR optical setup. At the same time, we would like to acknowledge Dr. Kim for setting up this optical path for mid-IR generation and getting us a good start on future experiment. Because the OPA output is adjusted to be diverging by the manufacturer for safety reason, the 3000 nm laser beam also exhibit an increment in size. To decrease the energy lost due to this widening, we place the 1st focusing lens right before the 2nd delay stage to slightly focus the mid-IR so it will not expand larger than our mirrors and lens downstream. When the 3000 nm pump enters the chamber via high-transmission viewport, it sustains intensity greater than 4 µJ/cm2. 106 6.4 Ice/water Deposition on Substrate Using Molecular Beam Doser In order to preserve the pristine property of the sample, in surface science it is common to grow, synthesize, or deposit the desired sample in-situ to the substrate in the same location or environment where the experiment would be conducted. To study ice/water in our UEC setup, depositing the water directly to the substrate in a UHV chamber is the only viable but very challenging method [Rua 2004], especially because we cannot use an enclosed cell to hold water sample because we need to preserve the direct access and exit path for the electron beam to sample. In addition, delivering water without damaging the 30 kV electron gun, mass spectrometers, and ionization gauges in the same UHV chamber is not a trivial matter. In 2007, Dr. Murdick, an alumni from our group, installed the molecular beam doser with fine and quantitative control of delivering molecular gas onto the surface under UHV[Mur 2009]. To determine the proper sample temperature for the experiment, we first perform a few dosing tests and monitor the water traces reported by our quadrupole mass spectrometer (QMS). By varying the dosing time, we deliver a variable amount of water onto our sample holder at < 100 K, then we warm up the sample holder temperature slowly, ~1 K / min, while recording the QMS readings for water, or at the mass-to-charge = 44. The result, plotted in Fig. 6.4.1, shows the ice/water starting to desorb or sublimate from the sample holder at ~140K consistently, regardless of the amount of water in the system. The total amount of water detected by the QMS, total area under the curve in Fig. 6.4.1, is proportional to the dosing time with a constant dosing rate. With more water dosed onto the sample holder, the shift in the overall profile in the desorption measurement with respect to the sample holder temperature can be rationalized by the thicker layer of water that would require higher temperature to desorb completely. With this universal desorption temperature, 140K, we can calculate the sublimation pressure using the formula in the literature [Wag 2011], 107 Figure 6.4.1 The water sublimation measured by from QMS as temperature rises with different dosing time. with where and with and the values of the normal triple point (Solid-Liquid-Gas). Using the sublimation pressure ; and are 140 K for Eqn. 6.4.1, we calculate torr, which agrees very well to the pressure measured by ion gauge in our UHV chamber. The water can be dosed onto many substrates of choice, depending on the desired experiment geometry, explained in section 6.2. For reflective diffraction geometry, we have successfully deposited water on pure silicon, silicon oxide, nanocavity on silicon, graphite, and on to a gold nanoparticle decorated silicon substrate. Visually, the ice/water layer can be observed on a pure silicon substrate, shown in Fig. 6.4.2 (b), comparing to the pristine silicon chip before dosing, shown in Fig. 6.4.2 (a). For 108 (a) (b) (c) (d) Figure 6.4.2 The pure silicon mounted on sample holder (a) before and (b) after water dosing. (c) Optical image of thin amorphous silicon membrane (blue area) manufactured on a silicon substrate (grey background). (d) Thin amorphous silicon membrane sample mounted (circled in red) onto our sample holder ready for transport into our UHV chamber for transmission diffraction experiments. the transmission diffraction geometry, we can deposit water on a thin layer (20nm) of amorphous silicon film that was originally intended for suspending samples for TEM observation, shown in Fig. 6.4.3. The deposition process can be monitored more precisely by the electron diffraction pattern from the sample using a glazing angle. For example, when water is deposited on the AuNP decorated silicon substrate, the diffraction pattern from AuNP will get obscured when nanoparticles are covered by the dosed water and ice, shown in Fig. 6.4.3 (a), (b), and (c). The same observation can be made during 109 (a) (b) (d) (h) (c) (e) (f) (i) (g) (j) Figure 6.4.3 Pictures from water experiment. (a) The diffraction pattern from AuNP decorated silicon substrate at room temperature. (b) When the amorphous water starts to cover the AuNP and obscure the AuNP diffraction, water dosing can stop, taken at T = 115 K. (c) A few hours after water dosing is stopped, the amorphous water self-assemble into crystal form at 115 K. (d) Diffraction pattern from silicon with nanocavity at room temperature. (e) Scattering from water starts to replace the nanocavity pattern, taken at T = 78 K. (f) Fully crystallized water completely cover the Si substrate with nanocavity, taken at T = 127 K. (g) Diffraction pattern of ice yields to that from Si nanocavity when ice starts to sublimate at T = 157 K. (h) The diffusive diffraction pattern from amorphous silicon membrane at T = 115 K. (i) Diffraction pattern from ice and amorphous silicon membrane. (j) SEM image of nanocavity on silicon substrate. 110 dosing water onto other substrates in the reflective diffraction geometry, like silicon with nanocavity, shown in Fig. 6.4.3 (j). The diffraction pattern from the substrate is replaced by the random scattering from amorphous water layer first, then completely obscured by the diffraction pattern after the amorphous water self-assembles into crystal ice, illustrated in Fig. 6.4.3(d) to (g). In the case of water crystal or ice transmission diffraction experiments using an amorphous silicon membrane, the electron beam would penetrate all the sample in its path, and the diffraction pattern recorded on our CCD camera is the sum of that from the membrane and ice crystal, illustrated in Fig. 6.4.3 (h) and (i). 111 6.5 (a) Ice/Water Experiment Result (b) Figure 6.5.1 Reflective diffraction experiment on water. (a) Reflective diffraction geometry with ice deposited on pristine silicon and typical diffraction pattern from ice layer. (b) Intensity ratio dynamics of ice (111) + (200) triggered by 3000nm laser, f = 4.5mJ/cm2, at T = 130K. Because the larger footprint of a probe on the sample can lead to a larger pump-probe spatial overlap and more diffraction signals from the wider sampling area, we start conducting the experiment using 3000 nm excitation laser on ice in reflection geometry, depicted in Fig. 6.5.1(a). With 4.5 mW power delivered on the ice surface and an expected 300 µm width in size, the mid-IR laser applies fluence ~ 4.9 mJ/cm2 on the ice layer at T = 130 K. As presented in Fig. 6.5.1(b), the change of intensity at the ice (111) + (200) ring, or the first intense ring shown in the diffraction pattern in Fig. 6.5.1(a), shows a fast decay and recovery that yields the sign of lattice fluctuation. The whole dynamics of decay and recovery took less than 15 ps to complete and exhibit a maximum of ~ 4% change in the integrated intensity of that ice (111) + (200) ring. However, due to the low power of the mid-IR laser and the smaller excited/probed area ratio inherent in the reflective experiment geometry, we could not generate higher change in order to examine this dynamics in detail. The main advantage of the reflective diffraction geometry is being able to cover a large sample area using a glazing incident angle for electron beam. Although the large footprint, which can be as greater than 1.7 mm long with a 30µm electron beam and 1o incident angle, provides stronger diffraction intensity by sampling larger area, it would 112 (a) (b) Figure 6.5.2 Transmission diffraction experiment on water. (a) Geometry of transmission diffraction experiment. (b) Diffraction profile obtained before (red curve) and 2 ps after (blue curve) the excitation laser hits the ice sample. The +2ps profile has been scaled to compare with that before mid-IR lands on sample. almost necessarily require a larger pump laser to excite the longer sampled area. With enough pump laser power, we can expand the size of the excitation laser on the sample surface so most of the sampled area is excited in order to obtain a high signal of reaction from material. With finite laser power, we can choose to excite a smaller area with higher fluence or a broader area with weaker fluence. Either scenario, however, would still generate less-than-desired signal when working with a less powerful excitation laser, for example our mid-IR, 3000nm laser. With the transmission diffraction geometry, depicted in Fig. 6.5.2(a), we expect the probed area can be fully covered by our 300µm mid-IR pump since the sampled area is the same size as the probe, ~ 30µm in diameter. With the electron beam penetrating through the ice layer and the amorphous silicon membrane, the diffraction pattern presents a 3/4 circular powder diffraction rings on our CCD camera, shown in Fig. 6.5.2(a). Since we have the diffraction pattern of the amorphous silicon membrane itself, shown in Fig. 6.4.3 (h), we can obtain the diffraction intensity solely from the ice layer by subtracting the contribution generated from the silicon membrane. Fig. 6.5.2(b) displays the radially integrated diffraction intensity from the ice layer showing the profile of the diffraction pattern before the excitation 113 laser illuminates on the sample (red curve) and the change in intensity observed at +2 ps after the mid-IR hits (blue curve). For comparison, we multiply the change in diffraction rings 33 times to show the observed change at +2 ps is indeed that from ice layer. The results translates to a ~1% drop in ice diffraction intensity after our 3000 nm laser illuminates the surface. However, the experiment time cannot be sustained long enough for us to study this dynamics in detail due to the excess vibration in our sample cooling mechanism. The sample used in our experiment is mounted at the very end of > 5' long cryogenic column, and the minute vibration at the motor that cycles helium gas into the cooling column is amplified at the sample end. A rough measurement yields a > 40µm vibration at the sample surface, which is sufficient to displace the sample out of the electron probe or change the fluence on the surface dramatically by moving the sample away from the peak of pump profile. From the optical constants of water reported in literature [Hal 1973], which states the extinction coefficient of water with 3000 nm laser is 0.272. The absorption coefficient can be calculated via 11388 cm-1, and this value leads to a ~5% absorption if we consider a 50 nm thick ice layer. Then the expected temperature change of a 50 nm thick ice layer, specific heat 2.03 J/goC, when illuminated by a fluence ~ 5mJ/cm2, 300 µm wide, 3000 nm laser is less than 0.1 K. Without having a higher power of 3000 nm laser, we can try to study a thinner ice layer, which may lead to lower diffraction intensity, while at the same time conduct the experiment at a temperature closer to the sublimation point, ~140 K. By combining 1) the high brightness electron beam already realized by the UEM project in our group, which can provide sufficient diffraction intensity from a thinner ice sample, 2) the base temperature closer to sublimation point, and 3) the low-vibration cryogenic system, which is already implemented in the 1T-TaS2 experiment described in chapter 5, we should then be able to elucidate on the age-long questions concerning the two-structure water in the near future. 114 CHAPTER 7 Surface-Plasmonic-Resonance Enhanced Interfacial Charge Transfer Interfacial charge transfer has been hard to monitor because of the fast time scale of carrier transfer, the meso- or nanoscale dimension, and the difficulty creating a reliable metal contract for electrical measurement. In this chapter, we present our photovoltammetry technique that allows us to quantitatively measure the charge redistribution, the direction of carrier flow, and the sequence of events at a heterogeneous interface that contains three elements: gold nanoparticle, silicon, and an ice/water layer. 115 7.1. Introduction To understand the fundamental processes in the new type of solar cells and photocatalysis that incorporate nanomaterials [Gra 2003] [Har 1997] and molecularly engineered interfaces [Ash 2002], it is important to be able to characterize the photoinduced charge dynamics in the nanostructures and interfaces. These photo-driven devices utilize the interface-induced carrier separation to minimize the recombination of the photogenerated electron/hole pairs and improve the sensitization by the visible light spectrum through controlling the size, dopant, and surface plasmonic effect [Shi 2000] [Mil 2004] [Luq 2007] [Les 2007] [Kon 2008] [Hua 1997] [Cal 2004] [Bac 1998] [Aro 2001]. At the nanomaterial interface, the migration of carriers from the sensitized interface region to the metal contact is driven not only by the local electrochemical potential difference, but also by the decay rate of such photoactivated carriers in the transport process. As the device dimension approaches several nm scale [Ada 2003] [Avi 1974] [Avo 2007] [Bez 1997], shorter than the mean free path of electron, ballistic transport becomes the dominant channel, the carrier trapping and recombination at the interface becomes the central issue to investigate [Mar 1985] [Che 1993] [Dat 1995]. These processes are difficult to characterize directly due to the fast time scale, minute dimension, and problems associated with forming reliable contact for electric measurement. While several ultrafast optical techniques have been applied to investigate the electron dynamics at the interfaces [And 2005] [Mil 1995] [Kub 2005] [Pen 2005] [Tan 2012], they are usually not well tuned to measure the photo-conductivity at the interface. Using the sensitivity of the diffracted electron beam to the local electric field, or ultrafast diffractive photovoltammetry technique [Mur 2008] [Rua 2009] [Cha 2011], we can observe the charge redistribution processes at nanomaterial interfaces induced by photoexcitation without contact at ultrafast time scale. With our photovoltammetry, we investigate three prominent charge transport process, depicted in Fig. 7.1.1: (1) Dielectric realignment: the alteration of alignment of dipolar elements, in dielectrics creates displacement filed without carrier current in the materials. (2) Carrier diffusions: the photocarriers 116 (a) (b) (c) Figure 7.1.1. Charge redistribution at interface after photoexcitation. (a) dielectric realignment. (b) carrier diffusion. (c) interfacial charge transfer. generated in the photoexcited region diffuse to the unexcited region and induce internal photocurrent. (3) Interfacial charge transfer: The photoexcitation alters the balance of chemical potential at the material interface, resulting the change transfer to counteract the change in free energy. The decay of these photovoltages may involve drift, dipolar relaxation, carrier recombination, diffusion, and radioactive decays. 117 7.2. Ultrafast Diffractive Photovoltammetry Methodology and Experiment Setup The experiment setup for the ultrafast photovoltammetry is the same as the ultrafast electron crystallography with reflective diffraction setup (see section 6.2.). The only difference is the method of data analysis. At the core of the photovoltammetry measurement, the link between photocurrent and the responding transient surface voltage is established via field integration. To evaluate , we consider a slab geometry, Fig. 7.2.1., that provides a basic framework for describing the transient-fieldinduced refraction of the diffracted beams. In the simplest concept, our photovoltammetry measures the photoinduced surface field that is required to "refract" or "bend" the diffracted electrons. In Fig. 7.2.1, the top trajectory is the electron scattering from the crystal planes without the presence of a surface field. The electron beam with initial energy e , incident at When a surface potential , is Bragg scattered at , exiting the surface at . , created by the charge redistribution that induced from photoexcitation, is presented in the electron path, the incident electron beam would be refracted deeper into the crystal at . The Bragg diffracted beam would get affected the same way and the electron beam would ultimately exit the crystal at with a net shift relative to on the CCD. The induced angular shift in the diffraction pattern can be calculated by 7.2.1 where 7.2.2 7.2. 118 Figure 7.2.1 The slab model for transient surface voltage. It is important to note the difference between the refraction-induced shift and the structurally relevant shift. The shift in the reflection peak position, following Bragg's law, should increase linearly with the scattering order in the reciprocal space. In contrast, the refraction-induced shift nonreciprocal relationship with respect to the exiting angle would show a More detailed derivation and discussion on ultrafast diffractive photovoltammetry can be found in our publication [Cha 2013]. The experimental setup for measuring surface voltages of nanoparticles and interfaces is similar to those described in section 6.2, but replacing the pure silicon with a nanoparticle decorated Si surface. As described in section 6.4., we deliver a layer of water-ice on the nanoparticles by vapor dosing at 90K using the doser. The steady growth of ice is monitored by the glazing incident electron beam until the signal of the gold diffraction is replaced by an ice pattern. This gives the rough estimate of the thickness of water-ice layer to be around 50nm, or roughly the same as the diameter of AuNP particles. 119 7.3 Charge Transfer between Nanoparticles and Substrate Enhanced by Surface Plasmon Resonance Excitation with the Coverage of Water-Ice The application of a water-ice layer that completely covers the nanoparticles-decorated interface can alter the incident photon resonance structure with the evanescent SPR field strongly coupled to the dipole moments of the surrounding water molecules. The modified resonance structure will impact the SPR-induced charge carrier dynamics, and it has great impact in searching the optimal geometry to enhance the performance of composite photocatalysis that incorporates semiconductor and plasmonicmetal nanostructures. Recent studies found strong positive correlation between SPE and reaction rate, leading to a hypothesis that the metallic SPR enhances rates of photocatalytic reaction at nearby semiconductor surface through carrier redistribution at the interface [Lin 2011]. With a sample of the Au nanoparticle on silicon substrate covered with dosed ice/water, we examine various channels that energetic charge carriers travel at metal/semiconductor/water-ice interface. We can then understand SPR enhancement effects. We apply a scan of the pump laser wavelength from 800nm to 400nm using our optic parametric amplifier. Over a time span up to 1000ps, we deduce the surface voltage of the ice layer from the refraction shift of ice diffraction pattern, as described in section 7.2 and [Cha 2013]. The result of time vs. wavelength photovoltage response map is constructed as shown in Fig. 7.3.1. From the time-slices across the map at representative = 400, 470, 525, and 585nm, the spectral evolution can be seen as encompassing two temporally separated process: one that commences at 0 ps and decays greatly within 100ps, and the second one that rises as the first one decays without relaxation at all within the observed time scale 1000ps. Slicing the response map at 30ps and 100ps, shown in Fig. 7.3.1(b), we see the photovoltage spectrum evolves from initially a singular peak at 525nm to 585nm at ~30ps, which mainly describes the fast process in dynamics across the spectrum. On other hand, at 120 (a) (b) Figure 7.3.1 Charge redistribution spectrum. (a) Surface photovoltage response map constructed using the diffractive voltammetry conducted on the water-ice surface covering gold nanoparticles/SAM/silicon interface at excitation wavelength from 400 to 800nm. Four selected surface photovoltage shown in white curves, at = 400, 470, 525, and 585nm, demonstrate a composition of two dynamics with different timescales. (b) comparisons between the surface voltage response spectra obtained from the interface without the coverage of water-ice (black line), ones with water-ice layer showing a red shift of the resonance peak (green line) at 30ps, and the bifurcation of peaks (blue line) at 100ps. ~100ps, the dual peak structure with an additional peak at 470nm presents the second process of the dynamics with different excitation wavelength. The shift of the dipole resonance peak from 525nm to 585nm can be understood by finite difference time domain (FDTD) simulation and contributed to a strong coupling between the SPR of the nanoparticles and the surrounding water dielectrics. However, the presence of high-energy response at ~470nm appeared at 100ps cannot be produced from the optical domain calculation alone. Such short-wavelength mode is typically of high-order and is not optically active at particle size less than 50nm. Figure 7.3.2 shows the result of the controlled experiment in which the photovoltage at the ice surface is measured without the presence of Au nanoparticles, in order to disentangle the two different dynamics observed in Figure 7.3.1(a). Without the Au nanoparticles on silicon substrate, we observe a 121 slow dynamics that is very similar to the second dynamics component with the presence of nanoparticles, but without the fast dynamics. This result reveals the slower process, red curves in Fig. 7.3.2, is in fact the charge carrier dynamics launched purely from the silicon substrate. Since the dielectric property of ice is unlikely influenced directly by visible light excitation, the apparent delay in the voltage rise on ice surface from the controlled experiments is indicative of a long-range charge carrier injection from Si into the ice surface. At the same time, the shortening of such an injection time as the photon energy increases, from 800nm to 400nm, is particularly interesting. The dependence of this delay on photon energy and the high charge drift velocity, ~1nm/ps, also support that the origin of energetic carrier injection is indeed from Si. When reaching the ice surface, the carriers dissipation takes a significantly a longer time (>ns). Near time zero, we also observe a small and nearly instantaneous downward refraction shift in every nanoparticles-free free experiment. We attribute this phenomenon to the shift in the chemicall potential at the ice/silicon interface due to photoexcitation, resulting in a swift change of the dielectric alignment of the ice layer. While the slow component in the surface voltage dynamics can be fully attributed to long-range charging from the substrate, the fast dynamics, plotted in blue circles in Fig. 7.3.2(b), which is completely absent in the nanopartilce-free controlled experiment, must be mediated by the nanoparticles directly. The surface field induced by charged Au nanoparticles can be measured on ice surface through dielectric realignment of the water molecules surrounding the nanoparticles. We can extract this fast charging dynamics by fully deducting the slow process in the controlled experiment from the overall dynamics, shown in Fig. 7.3.2(b). Since this fast dynamics reaches maximum before 50ps, the spectrum representing this long-range-charging by the spectrum-slice shown in green curve in Fig. 7.3.1(b) at 30ps. The red-shifting, from 525 to 585 nm, of this spectrum at 30ps indicates the charge transfer between the nanoparticles and the Si substrate is most efficiently driven by the localized dipole resonance fields at the interface between the two. Furthermore, since this peak at 585nm is present at the 100ps time scale, shown in blue curve in Fig. 7.3.1(b), this dipole resonance is also responsible for the elevation in the transfer of energetic electron to the ice surface. This is not surprising since the generation of energetic 122 (a) (b) Figure 7.3.2 Dynamics of induced charge. (a) The controlled experiment with the presence of AuNP for Ice/AuNP/SAM/Si photovoltage measurement. The rise of the surface voltage is delayed by the timescale of the charge carriers migrating to the ice surface after being generated from the Si substrate. (b) Equivalent results obtained the surface with AuNP decoration. By comparing to (a), we can deduce the fast components (blue circles) unique to the nanoparticles-decorated surface. carriers at Si surface can also be enhanced by the evanescent waves of SPR in the region. Lastly, it is also important to notice the appearance of the peak at 470nm in elevating the charge level at the ice surface indicates that the optically, spatially non-homogeneous higher moment SPR might be activated at the nanostructural interface [Mah 2012] [Sche 2012] [Che 2011]. Such a high-energy mode excitation, which is much weaker than the dipole resonance, can play a significant role in the surface charging response spectrum because the high-energy barrier required for the carrier injection into the ice conduction band (3.2eV above the Si conduction band edge) significantly suppresses the dominance of the dipole excitation over such a channel. The ultrafast photovoltammetry described here can provide direct characterization of charge transfer at device interface and nanoscale material. Without the interference of the metal contact that is required for electric measurement, the field-sensitive electron probe provides a clean observation of the 123 carrier dynamics at femto second time scale. The application of this diffractive voltammetry includes site-selected studies on nanostructured, SPR enhanced, or heterogeneous interfaces that is crucial in understanding the delicate play in carrier redistribution. 124 CHAPTER 8 Summary In the CeTe3 experiment, we have separated the dynamics of two order parameters from ultrafast structural response to intense optical excitation. From the well separated time scales shown in the structural suppression, we have concluded the periodically modulated ionic potential well has been preserved mostly intact during the sub-ps charge melting, hence it can facilitate the rapid recovery of the electronic order as proposed by others. We believe the well-separated order parameters are due to the significantly different effective inertia in these two subsystems, and the fact that charge ordering is directly coupled to the valance electrons that was directly elevated by our femtosecond laser pulses. The coupling between charges and ions can be reestablished once the hot electron temperature is cooled down so a stable CDW condensate can recover. We also conclude the fast channel has little to do with the specific CDW mechanism, which is universally observed by other reports with sub-ps recovery of charge ordering. Therefore, it is the slower ps structural response following the excitation at electronic part of CDW provides the distinctions that characterize the CDW family with the stretch of coupling between electrons and ions. In the case of CeTe3 that demonstrates a fluctuation-dominated phase transition represents the inherently Peierls-distorted electron-phonon system in CDW. With 1T-TaS2, a material exhibiting a Mott-Hubbard gap and a nesting-driven CDW gap, we have presented a new avenue to explore the energy landscape that was not accessible via conventional methods. With ultrafast photo-doping and carefully chosen excitation energy, we not only drive the 1TTaS2 to states previously discovered through chemical doping or high pressure treatments, but also push the material to other hidden states by traveling a different route on the energy topography. By reaching 125 these meta-table states at sub-ps time scale, we open up the possibility of application with high-speed low-energy consumption photonic and electronic devices. With the photovoltammetry technique that can measure charge redistribution and diffusion at interface quantitatively, we have explored the charge transfer at heterogeneous interface enhanced by surface plasmon resonance and coverage of ice. We have demonstrated that the technique can observe the minute charge transfer between three different materials in our sample: gold nanoparticle, silicon, and ice/water layer. With a flexible experiment setup, we were able to monitor charge redistribution with any combination of these three materials or as a whole, hence to pinpoint the source and flow of each charge distribution. At the same time, utilizing our tunable excitation laser and SPR phenomena of nanoparticles, we sequenced the charge transfer events that was not possible with other technique that requires metal contact for carrier measurement. With the capability to study water at its phase boundary, we have explored the possibility of observing the structural dynamics. We have observed a minute change in the ice structure but could not study the phenomena in detail due to limitation of laser power and excess vibration issue. However, we did learned valuable experience along the journey. With the low vibration sample holder already implemented and proven reliable when utilized in the 1T-TaS2 experiment and the high-brightness of ultrafast electron microscopy electron source realized by another project in our group, we can expect the exploration of water unique properties to continue and prosper. The next experiment following the result of CeTe3 is another anisotropic CDW material: ErTe3. Belonging to the same Rare Earth tritellurite family, ErTe3 presents two seemingly independent CDW formation each with its critical temperatures. With ErTe3, we are posed to examine the role of symmetry breaking, electron-lattice coupling, even CDW-CDW interference with this new material. Regarding the phase transformation of CDW material, or 1T-TaS2 in particular, we plan to add another dimension to the phase diagram by studying the doped 1T-TaS2 which has shown a superconducting phase emerging. With the intimate relationship between CDW and superconducting, one may be able to unveil the cooperation or the competition between two orders with have-it-all 1T-TaS2. 126 APPENDICES 127 Appendix A Electron Counting and Statistical Uncertainties (a) (b) Figure A1 Analysis on electron count. (a) The discrete single-electron events recorded on a CCD camera. (b) The number of occurrences of single-electron events as a function of digital counts recorded for these events. A mean value of 989 is determined as the analogue-to-digit unit, used to convert the CCD signals into the electron counts. To evaluate the statistical uncertainty of the experiment, electron counting is conducted. The single-electron counting events are established with attenuated electron beam, which are recorded on the CCD detector, as shown in Fig. A1(a). A total of 1005 such events are counted, and the occurrence of single-electron events as a function of their digital counts recorded on the CCD is depicted in Fig. A1(b). The distribution has an average value of 989 digital counts per electron, which we assign as the analogueto-digit unit (ADU), used to convert the CCD intensity to electron counts. The number of the electrons associated with diffraction intensities from which an uncertainty statistics. at thus can be calculated using is determined for , based on the Poisson counting is derived by integrating the digital CCD intensity around the respective diffraction peak, with the background (thermal noise, incoherent scattering) subtracted by a 2 nd order polynomial fit. Fig.A2(a) shows the distribution of data at each time stance for the CeTe3 experiment, discussed in section 4.2, with data acquisition time ranging from 103-104 sec. Long integration time is used on 0-2 128 (a) (b) (c) Figure A2 Statistic on electron counts. (a) The data integration time used for each time stance under laser fluences F=2.43, 4.67, 7.30 mJ/cm2. (b) The absolute integrated intensity evolution of CDW superlattice peak in unit of electron counts. (c) The absolute integrated intensity evolution of main lattice peaks at (0,4) extracted from the same diffraction images as (b). ps data points to provide sufficient signal-to-noise ratio to investigate the short-time responses. In order to differentiate the fluctuation effects that have a strong anisotropy, all the reported are extracted from isolated peaks without averaging equivalent peaks that has the same symmetry at the ground state. Fig. A2(b) and (c) show of electron counts. and obtained under three different fluences in unit is extracted from the superlattice peaks at is ~103 e-, while for main Bragg peak ~105 e-. is from lattice Bragg peaks at (0,4). The typical We note that at F=7.30 mJ/cm2, , and drops to as low as a few hundred e- counts at ~ 5 ps, resulting in a relatively large statistical uncertainty. 129 Appendix B Two Component Fitting and Statistical Analysis Figure B1 The zoomed in plot of satellite intensity of CeTe3 at early times showing two-step suppression. The data from F=2.43 mJ/cm2 are multiplied by 3 to compare with data from F=7.30 mJ/cm2. The error bars are calculated based on the counting statistics described in Appendix A. Fig. 4.1.3(a) and Fig. B1 shows the suppression of satellite intensity of CeTe3, expressed in terms of normalized intensity , where is obtained by averaging the negative time from F=2.43 mJ/cm2 experiment is scaled up by a data (t=-5ps to -1 ps). In Fig. B1 the factor of 3 to compare with from F=7.30 mJ/cm2. The inhomogeneity in the decay of signals is evident from the nonscalability between the two fluences. Both datasets contain a component with a sub-ps decay and a slower ps component is clearly visible, especially in F=7.30 mJ/cm2 dataset. To describe the different timescales in the suppression of , we fit with a model consisting of two independent exponential decays and recoveries:  r1    A1    exp  t  to  /  r1   exp  t  to  /  d 1     r1 d1 f t   1   ,  r 2  exp  t  to  / r 2   exp  t  to  / d 2   A2      r2 d2   130 (B1) where A1 and A2 represent the amplitude of the two-components, represent the respective decay and recovery times of the two components, and t0 is the onset time. f(t) is coarse-grained by numerical convolution with a pump-probe cross-correlation function fcc(t), which is modeled as a Gaussian f CC  1  CC 2 et 2 2 / 2 CC , where =170 fs is the half-width of electron pulse, estimated based on the FWHM electron pulse-width: 390±110 fs (Fig. S2). t0, as determined from the fitting, can shift as much as 200 fs relative to the ZOT established from graphite and between different CeTe 3 m datasets, which is attributed to the fluctuation of the sample stage ps during the time- consuming experiment. The best two component fit on the F=7.30 mJ/cm2 dataset, as depicted in Fig.B2(a), yields un-coarse-grained A1/A2=0.28. Clearly, and = 350±150 fs, = 570±200 fs, = 3.8±1 ps, and a ratio are largely resolution-limited, however, the large disparity of the timescales associated with the two components permits a generally robust determination of the relative contribution A1/A2. increases at lower fluencies. The validity of two component model is checked by adjusting A1 from 0 to beyond the best fitted value to assess the difference in is fixed while other parameters are determined (except , tr1, t0) by fitting. Since at A1=0, Eqn. B1 reduces to a single component model, which has a significantly larger =0.28±0.07, as shown in Fig, B2(b). The optimized t=-2 to 20 ps), which yields a reduced , defined as . In this exercise, A1 than that of the best fit at has a value of 16.5 (with 15 data points from /(number of data points), nearly 1, indicating that two component model is statistically sound. The standard deviation = 0.07 associated with A1/A2 is calculated based on [Bev 1992]:  2 2   2  2 2   a  131 (B2) (a) (b) 45 1.0 2 F=7.30 mJ/cm A1+A2 A1 A2 35 2 Best single component fit 0.6 30  S1(t)/S1(t<0) 0.8 F=7.30mJ/cm S1/S1 data fit 40 2 Best two component fit 25 0.4 20 0.2 15 min=0.28 ± 0.07 -1 0 1 2 3 4 5 6 7 8 0.0 0.1 Time (ps) 0.2 0.3 0.4 0.5 0.6 a=A1/A2 Figure B2 Two component fit. (a) The results of two component fit of experimental S1(t)/ S1(t<0) data at F=7.30 mJ/cm2 (blue: total, red: first component, black: second component). (b) The value as a function of =A1/A2 based on fitting S1(t)/ S1(t<0). In contrast, 2 determined at the single-component limit is more than 3 away, representing a less qualified model. We find that datasets from different fluencies can be fitted with nearly the same values, but different and (ranges from 2.5 ps at F=2.43mJ/cm2 to 3.8 ps at F=2.43mJ/cm2). Overall, our results from CeTe3 experiment support the existence of a sub-ps component in the depression and recovery of PLD, which is directly responsive to the corresponding sub-ps suppression and recovery of electronic counterpart (CO), widely observed in CDW systems using ultrafast optical and angle-resolved photoemission spectroscopy techniques. 132 Appendix C Carbon Nanotube Sample Preparation A suspended carbon nanotube sample on TEM grid has been implemented and the procedure of obtaining such a sample is outlined below. A few optical and electronic images are also presented in Figure C1 1. The multi-wall carbon nanotube (MWCNT) is purchased from Nanolab, Inc, with specification of 15±5 nm in diameter, 5-20 µm in length, and -COOH group functionlization (part number PD15L5-20-COOH, $130/g). 2. The as-purchased MWCNT material is first suspended in orthodichlorobenzene (ODCB) in a concentration of 1.5mg per 5g of ODCB. Then the solution is sonicated for 1 hour. 3. Then the sonicated solution is further diluted with concentration of 5 drops per 9 g of ODCB. 4. Sonicate the diluted solution for another 30 minutes until the MWCNT solution contains no visible solute. 5. The MWCNT can be transferred to a TEM by delivering a few drops of the solution after step 4 onto a TEM grid that is positioned on a filter paper, which helps to guide the solution through the TEM grid. 6. The density of MWCNT on the TEM grid can be controlled by adjusting the number of drops applied to the grid. 133 (a) (b) (c) (d) (e) (f) Figure C1 Images of MWCNT. (a) Suspended MWCNT on copper TEM grid. (b) TEM image of a suspended MWCNT on TEM grid. (c) SEM image of a MWCNT deposited on holey carbon TEM grid. (d) SEM image of a MWCNT deposited on holey carbon TEM grid. (e) Diffraction pattern from a MWCNT. (f) Individually separated MWCNT on thin Si membrane. 134 Appendix D Tsunami Alignment Figure D1 Tsunami fs configuration The procedure described here should be treated as a supplement to the information in the manual provided by Spectra Physics. One should read the manual first then use the information provided here as an aid. 1. Supplement to Front-End Alignment, page 6-2 in the manual. a. As described in the manual, DO NOT adjust the focus of M3 and M4. b. Pump beam from Millennium Pro should be positioned at the center of P1. c. Direct pump beam using P1 and P2 so the pump is centered on the side of M3 and M4 that is CLOSER to the Ti: sapphire rod. This step is crucial to ensure the ease of further alignment. The pump beam does not need to be located at the center of P2. It is been observed that the pump beam is usually above the center of P2. d. Be careful not to put anything in the path of beam near Ti: sapphire rod since it is highly focused there. 135 From M3 From M1 Figure D2 Two IR images on M4. e. Use M2 to center the pump beam on M1. f. There should be two IR images on M4. Unlike described in the manual on page 6-7, the image from M3 is a rectangular shape while the one from M1 is a horizontal-orientated rectangle. (See Fig. D2) g. One can move the M1 image with M1 and both images with M3. h. Once these two IR images are positioned on M4, one can remove M4 and view these two IR images better on wall of the output bezel on figure 4-3 in manual. i. The proper location of these two IR images has been marked on the output bezel with marker as a guide. j. Place M4 back once step h is completed and proceed to Cavity Alignment for a FS System on page 6-7 in manual. 2. Supplement to Cavity Alignment for a FS System, page 6-7 in the manual a. Center two IR images on M5 using M4. This step is critical to provide enough travel of M5 to start lasing. b. Using M5, guide IRs through Pr1 to Pr4, to AOM, then finally M10. The IRs should go though Pr1 and Pr4 at the same distance from the edge of each prism. 136 c. If needed, one can remove the beam splitter at the outside of output of Tsunami and observe two IRs at ” away from Tsunami output. Adjust M to center IR spot to the IR square background. d. Adjust M10 to start lasing. The output power of Tsunami should increase significantly once lasing starts. e. Adjust M1 and M10 to optimize output power. f. Follow manual to optimize photodiode location and mode-lock. 137 Appendix E Optimization at Spitfire for Optimal Output of Mid- IR Laser 1) Be sure the pulse train on oscilloscope looks sharp with minimal side peaks on the side of main pulses. If not, pulse train can be optimized by a) With Ch1 on and Ch2 off, adjust delay zero in timing menu (service-level control required) so the pulse train is as far left as possible on scope. b) Adjust Ch1 so the small peaks between main pulses are minimized. 2) Adjust Ch1 and Ch2 so the build-up time of pulse train is ~62ns. (Measured from the first peak to the highest one). The shorter build-up time may not provide the highest output from Spitfire, but it will generate higher TOPAS and 3000nm output down the line. 3) Optimize 266nm output from Tripler with motorspeed. 4) Optimize output from TOPAS with motorspeed, which may be slightly different from that from step 3) 5) Optimize output from TOPAS with the mirror before TOPAS entrance. 6) Optimize output from TOPAS with time-plate on the side of TOPAS. 7) Optimize 3000nm power by adjusting signal-idler overlap on crystal and delay stage of idler. 138 Appendix F Gold Nano-Particle Deposition on ITO 1) Clean several large glass beakers with Alconox and rinse well with distilled water (DIW) generated by physics department . 2) Sonicate the needed glasses and Teflon wares in these large glass beakers for 2 minutes and remove these wares with new gloves onto new kimwipes. 3) Rinse large glass beakers with some Acetone, then sonicate all wares in Acetone for 2 minutes and remove them with new gloves onto new kimwipes. 4) Sonicate ITO substrate in Acetone, Alconox in DIW, and DIW for 15mins each. 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