The focus of this work is the study of processes at the edge of the current space and time resolutions. This includes both efforts in the development of an ultrafast electron microscope (UEM) and in the study of correlated electron systems that reflect measurements taken with this instrument.The development of a reliable ultrafast electron diffraction and imaging system requires a low emittance source of photoemitted electrons and an understanding of how the properties of the generated bunch depend on the photocathode properties. In order to gain more understanding of this process, we combine the so-called three-step photoemission model with N-particle electron simulations. By using the Fast Multipole Method to treat space charge effects, we are able to follow the time evolution of pulses containing over 106 electrons and investigate the role of laser fluence and extraction field on the total number of electrons that escape the surface as well as virtual cathode physics and the limits to spatio-temporal and spectroscopic resolution originating from the image charge on the surface and from the profile of the exciting laser pulse. The results of these simulations are compared to experimental images of the photoemission process collected using the shadow imaging technique. By contrasting the effect of varying surface properties (leading to expanding or pinned image charge) and laser profiles (Gaussian, uniform and elliptical) under different extraction field strengths and numbers of generated electrons, we quantify the effect of these experimental parameters on macroscopic pulse properties such as emittance, brightness (4D and 6D), coherence length and energy spread. Based on our results, we outline optimal conditions of pulse generation for UEM systems.With our knowledge of the photoemitted pulse properties, we also present our development of a design for the whole UEM column using the Analytic Gaussian model. We summarize the derivation of the equations governing this mean field model and show how the contributions due to the photoemission gun and the relativistic motion of the electrons can be added to this formalism to make it applicable for our system. We then explain the procedure used for optimizing the lens and RF cavity strengths and analyze both the effect of each separate optical element and their role in the column. We discuss the limits of this model and calculate the achievable temporal and spatial resolutions under different photoemission conditions.We conclude the present work with an investigation of Tantalum Disulphide (TaS2), a material that presents interesting ultrafast phenomena that can be probed using the UEM. TaS2 is a transition-metal layered compound that for T<190K displays a commensurate charge density wave (C-CDW) phase characterized by insulating behavior with the opening of a gap at the Fermi energy. To better understand the C-CDW phase and explain its quantum mechanical origin, we perform density functional theory calculations of the electronic band structure of 1T-TaS2 and quantify the effect that spin orbit coupling and Hubbard repulsion have on the ground state. Our results show that neither of these interactions is sufficient to reproduce the insulating gap seen in experiment, an observation which is confirmed by our calculation of the phonon band structure and absorption spectrum. We also consider the effect of different stacking configurations of the TaS2 layers and find evidence of gap opening for bilayers in the presence of disordered stacking.
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