Theoretical Study Of Electronic Structure Of Some Two-Dimensional Topological Materials

At present,a hot research field in condensed matter physics is to explore and classify different topological phases in real materials.The bulk phase of topological materials is nontrival,manifesting special boundary states(or surface states)on the boundary(or surface).These states are playing important roles in spintronics and quantum computation.Among them,the structure of two-dimensional topological materials is relatively simple,which is easy to study,and their carriers are confined in two-dimensional plane,producing other exotic properties.In this thesis,we carry out theoretical study and design on electrical properties of several different two-dimensional topological phases.The main contents of this thesis are as follows:Chapter 1 mainly reviews the research progress of several different types of topological materials in detail,including traditional first-order topological insulators,new higher-order topological insulators and topological semi-metals.Chapter 2 mainly introduces density functional theory and tight-binding model method,as well as the software used in our work.Starting from chapter 3 to chapter 5,we present the details of the work we have done.In chapter 3,using first-principles calculation and tight-binding model method,we calculate the topological properties of the two-dimensional carbon-based materialγ-graphyne.The calculation results show that γ-graphene is a two-dimensional quadrupole topological insulator with a large band gap(-0.94 eV).As a second-order topological phase,γ-graphene has three essential characteristics of two-dimensional quadrupole topological insulator:quantized bulk quadrupole moment,gapped topological edge state and gapless topological corner state.Moreover,the gapped topological edge state just exists at the armchair-type ribbon with-C≡C-as termination,and the gapless topological corner state only exists at the corner with 120° termination,which can be explained by different edge hopping textures and corner chiral charge,respectively.In addition,the topological corner state is stable even taking finite disorder into account,and its energy level does not change with the system’s size,indicating that the topological corner state is very robust.In chapter 4,combining tight-binding model,recursive Green’s function method and Lanczos recursive method,we study the topological properties of the two high-energy band gaps induced by interlayer coupling in van der Waals-coupled two-dimensional twisted bilayer material.Generally,with the decrease of twist angle,the coupling between layers in material will increase,which flattens the low-energy band in band structure and separates them by two high-energy band gaps.The two high-energy band gaps correspond to full filling and zero filling of the low-energy band in transport measurement.The study find that twisted bilayer graphene and twisted bilayer boron nitride are both two-dimensional second-order topological insulators in the full filling and zero filling band gaps,and both of them have the three essential characteristics of two-dimensional second-order topological insulators,namely,non-zero bulk topological index,gapped topological edge state and gapless topological corner state.In particular,the two second-order topological states exist in a wide angle range,and the topological corner states are robust to microscopic structure disorder and the choice of twist center.In chapter 5,we design three patterned two-dimensional electron gas models possessing different kinds of two-dimensional non-symmorphic symmetry(wallpaper group p2mg,p2gg and p4mg,respectively).Both symmetry analyses and numerical calculations reveal that external non-symmorphic symmetry will induce rich topological band-crossings in the system:when only intrinsic spin-orbit coupling is considered,the system would own fourfold-degenerate Dirac nodal-lines,which is a Dirac nodal-line semi-metal;when intrinsic spin-orbit coupling and Rashba spin-orbit coupling are considered simultaneously,the Dirac nodal-line would disappear and hourglass Weyl points emerge.Finally,in chapter 6,we summarize the main conclusions of this thesis,and present a brief outlook for the future studies on novel topological materials.