First-principles Study Of Edge States In Two-dimensional Dirac Semimetal And Quasi-particle Interference Of Topological Surface States

Since the 21st century,the topological state has been one of the most impor-tant frontier topics in condensed matter physics.Topological insulators,topological semimetals,magnetic topological insulators,etc.have sprung up,greatly enriching people's understanding of the macroscopic quantum state of matter.This thesis mainly studies the edge states of Dirac semimetal and quasi-particles interference of topologi-cal surface state.We take two-dimensional transition metal sulfides(TMDs)as an ex-ample to analyze the stable topological edge states.Quasi-particle interference pattern,as a simulation tool for studying the topological properties of topological insulators,has been studied in detail.In Chapter 2,we briefly reviewed the theoretical methods in band theory:first-principles calculations,k·p perturbation approximation,tight-binding approximation.Combination of theoretical derivation and numerical simulation,three methods often complement each other and play a vital role in the study of topological material states.In Chapter 3,based on first-principles calculations and structure search method-s,we and our collaborators predicted a new structure of two-dimensional TMDs-1H'phase.Taking 1H'Mo S₂as an example in our article,it has Dirac states protected by time inversion and space inversion.Related calculations show that 1H'phase has rich topological properties under strain:from topological trivial state to type II Dirac semi-metallic state,and then to the type I Dirac semi-metallic state.According to the bulk-boundary correspondence,we have calculated the topological edge state and then proved that it is very stable.Finally,it is extended to the other five TMDs systems(Mo Te₂,WTe₂,Mo Se₂,WSe₂,WS₂),we also plotted the topological phase transition diagram under strain.It is found that they have similar properties to Mo S₂,indicating that 1H'phase may be used in nanoelectronic devices and other fields.The fourth chapter mainly introduces quasi-particle interference of topological in-sulators.Quasi-particle interference patterns show the information in the k space(Bril-louin zone),which is very helpful to understand and verify the topological properties of the topological system.We firstly gave two theoretical derivation methods for quasi-particle interference patterns:T matrix and JDOS method.Then we took the topo-logical insulator Bi₂Te₃and the magnetic topological insulator Mn Bi₂Te₄as examples,and analyzed the quasi-particle interference on the(111)surface in detail based on non-magnetic scattering and magnetic scattering.It would have certain guiding significance for the development of scanning tunnel microscope.The last chapter is the summary of this thesis.