The Study On The First-principles Calculations Of Topological Materials And Their Topological Phase Transitions

With the rapid development in nearly 15 years,topological materials has become one of the most popular research fields in condensed matter physics.There are nontrivial symmetries protected surface(boundary)states on the surfaces(boundaries)of topological nontrivial materials.Their nontrivial topological properties are represented by the topological invariants and determined directly by the bulk band structures of systems,which are not affected by the perturbation such as disorder or impurity.Different topological invariants represent different topological phases,and the topological phase transition between different topological phases has also become a research hotspot in the field of topological materials.In this thesis,I first introduce the development history of topological materials in Chapter 1,including the quantum Hall effect family,topological insulators,topological crystalline insulators,topological semimetals,and topological quantum chemistry theory and symmetry-based indicator theory developed in recent years.I will introduce the diagnosis methods for topological phase of materials based on the theories.In Chapter 2,I mainly introduce the calculation methods used in the study of topological properties of materials,including the density functional theory,Wannier function method and the k·p model method.Then in Chapter 3 and Chapter 4,I introduce two works about topological phase transition of materials during my Ph.D.career,which can be divided into the topological phase transition process from trivial state to nontrivial state of magnetic layered materials and the topological phase transition from Weyl semimetal state to topological insulator state of nonmagnetic systems without inversion symmetry.Finally,in Chapter 5,I summarize all the research works I have done during my Ph.D.career and the prospect of the future research direction of topological materials.In Chapter 3,based on the first-principles calculations and theoretical analysis,we investigate the electronic structures,topological properties and conditions for topological phase transitions(TPT)of the magnetic layered compound MnSb2Te4.The calculation results indicate that the ground state of MnSb2Te4 with ideal structure is a trivial antiferromagnetic(AFM)insulator state.The band inversion can be realized by increasing the spin-orbit coupling(SOC)of Sb by more than 30%or shortening the interlayer distance by more than 5%,and this results in a TPT from a trivial AFM insulator to an AFM topological insulator or an axion insulator.For the ferromagnetic(FM)case,it is a normal FM insulator.The band inversion can happen when SOC is enhanced by 10%or the interlayer distance is decreased by more than 1%.Thus,FM MnSb2Te4 can be tuned to be the simplest type-I Weyl semimetal with only one pair of Weyl nodes.The Fermi arc connecting the projections of two Weyl points with opposite chirality can be observed on the side projected surfaces.In Chapter 4,we propose that the iso-structural compounds Cu2SnS3 and Cu2SnSe3 can be used to simulate the topological phase transition from a Weyl semimetal to a topological insulator.When spin-orbit coupling(SOC)is ignored,they are both the simplest nodal line semimetals with only one nodal ring in their crystal momentum spaces.The including of SOC drives Cu2SnS3 into a Weyl semimetal(WSM)state with only two pairs of Weyl nodes.In contrast,SOC leads Cu2SnSe3 to a strong topological insulator(TI)state.This difference can be well understood as there is a topological phase transition(TPT).Based on the calculation of Cu2Sn(S1-xSex)3 within virtual crystal approximation and an effective k·p model analysis,we find that in this TPT,the Weyl nodes are driven by tunable SOC and annihilate in a mirror plane,resulting in a TI.This TPT is accompanied by the evolution of Weyl nodes,the changing of mirror Chern numbers of mirror planes and the Z2 indices protected by time-reversal symmetry.We believe that the theoretical demonstration of controlling TPT and evolution of Weyl nodes will stimulate further efforts in exploring them.