| In this dissertation, our aim is to contribute to the understanding of edge properties of two-dimensional (2D) carbonic materials, including graphene and organometallic frameworks. A set of modeling and simulations, using first-principles density functional theory (DFT), tight-binding (TB) method, and molecular dynamics (MD) method, have been performed to (1) investigate the structural edge stability of graphene from both thermodynamic and kinetic points of view and (2) explore the existence of nontrivial electronic edge states, which carry nonzero topological invariant, in 2D organometallic frameworks. Specifically, this dissertation comprises the following four chapters of topics: (1) chemical versus thermal folding of graphene edges; (2) quantum manifestations of graphene edge stress and edge instability; (3) prediction of a two-dimensional organic topological insulator; (4) prediction of a large gap flat Chern band in a two-dimensional organic framework. Our work presented in the first two chapters not only has explained certain experimental observations on graphene edges, but also has been confirmed by other researchers' findings, both experimentally and theoretically. The studies shown in the last two chapters predict the existence of quantum spin Hall phase, a physical phenomenon that has been an exciting area of recent research in condensed matter physics, in 2D organometallic frameworks, a class of materials that are used to be mostly of interest to chemists. Therefore, we hope that these new findings could lead to a marriage of condensed matter physics and organic chemistry to foster an interdisciplinary research field, which will broaden the scientific and technology impact of topological materials. |
