Evolving from the macroscopic scale to the nanometer scale, inparticular by reducing the dimensionality, fundamental properties(such as electronic and mechanical properties) of certain systemsexhibit dramatic changes, which not only give rise to a wide rangeof emergent phenomena, but also boost technology developmentincluding nanoelectronics, optoelectronics and catalysis. In thisthesis, I utilized combined techniques including densityfunctional theory (DFT), molecular dynamic simulations (MD),continuum elasticity approach, and the tight-binding model toconduct a systematic study on low-dimensional nanostructuresregarding their electronic and mechanical properties as well asunderlying microscopic transformation mechanisms between differentstructural allotropes.First, I briefly introduce the motivation and background of thisthesis. Then, in Chapter 2, I describe the computationaltechniques, mainly the DFT approach, on which most of my thesis isbased.In Chapters 3 and 4, I apply the continuum elasticity method tostudy the phonon spectrum of two-dimensional (2D) andone-dimensional (1D) systems. My results highlight advantages ofthe continuum elasticity approach especially for the flexuralacoustic phonon modes close to the $\Gamma$ point, which areotherwise extremely hard to converge in atomistic calculationsthat use very large supercell sizes.From Chapter 5 to Chapter 7, I focus on allotropes of groupIII, V and VI elements and study boththeir stability and microscopic transformation mechanisms from oneallotrope to another. First, I predicted a stable phosphorus coilstructure, which may form by reconstruction of red phosphorous,and which was synthesized by filling a carbon nanotube withsublimed red phosphorus. Second, I proposed two stable 2Dallotropes of Se and Te. I also suggested and evaluated apromising fabrication approach starting from natural 1D structuresof these elements. After considering low-dimensional chargeneutral systems, I changed my focus to study the effect of netcharge on the equilibrium structure. Considering a heterostructureof alternating electron donor layers an monolayers of boron, Ihave identified previously unknown stable 2D boron allotropes thatmay change their structure under different levels of chargetransfer.From Chapter 8 to Chapter 10, I focus mainly on carbon-basednanomaterials and their properties. In Chapter 8, I proposed a wayto enhance the density of states at the Fermi level in dopedC60 crystals in order to increase their superconductingcritical temperature to room temperature. In Chapter 9, I haveinvestigated a shear instability twisted bilayer graphene usingthe tight binding model. This system is susceptible to very smallstructural changes, since it becomes superconducting in a verynarrow range of twist angles near the 'magic angle'. In Chapter10, I introduced the cause of an unusual negative Poisson ratioand a shape-memory behavior in porous graphene with anartificially designed pattern.In Chapter 11, I finally present general conclusions of my PhDThesis.
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