The Application Of Topological Band Theory In First-Principles Calculations

With their novel physical properties and potential physical applications,topologi-cal materials have attracted the attention of more and more condensed matter scientists in recent years.From the initial incomprehension of phenomena such as the quantum Hall effect to the present fact that a straw shows which way the wind blows,the devel-opment of topological theory has gone through a long process for more than a century.With the successive development of density functional theory,computational physicists can even calculate and predict thousands of topological materials with high throughput,providing a rich and diverse research platform for experiments and theories.In this thesis,firstly I will start with the development of topological theory in Chap-ter 1,to introduce the development process of related theories,the properties and clas-sifications of topological insulators,topological crystalline insulators and topological semimetals,and the corresponding topological invariants.Combining with the recently developed symmetry-based indicator theory,real space construction method,etc.,the diagnosis methods of topological materials are introduced.Secondly,I will review the development history of density functional theory and energy band theory in Chapter2,and give a brief introduction to the properties of the widely used Wannier function.Finally,as the main part of the thesis,I will introduce four projects about topological materials during my Ph.D.based on first-principles calculations.My research work can be roughly divided into two aspects:(1)Calculate and predict new topological materials.The project in this aspect is in Chapter 3 of this paper,on the study of the topological state of the HfRuP family super-conductors.In this part,I will introduce the topological and superconducting properties that we found in the HfRuP family.In experiments,we have verified the superconduc-tivity through resistance and magnetic susceptibility measurements and band structures of these materials.In theoretical calculations,we have obtained the band structures and topological properties of these materials.We found that the materials in this family can be divided into two types:one type is the type II Weyl semimetallic phase,including HfRuP;and the other type is the topological crystalline insulator phase,including Zr-Ru As,ZrRuP and HfRuAs.We predicted that this family is very possible to achieve topological superconductivity due to its topology and intrinsic superconductivity.(2)Exploit topological theory to explain the properties of the topological system and provide a new theoretical tool for finding new topological materials.The projects in this aspect are in the Chapter 4 on LaSbTe and the Chapter 5 on S₄ Weyl semimetal.In the work of LaSbTe,we found that the two topological phases of the layered material LaSbTe:weak topological insulator phase and topological crystalline insulator phase,can be obtained by layer construction,and the layer construction in real space and the topology of energy bands in momentum space have an one-to-one corresponding,which provides an example for understanding the physical nature of topological crystalline in-sulators and topological insulators.In the work on Weyl semimetals with the combined symmetry S₄ of rotational symmetry C₄ and spatial inversion symmetry,we propose a symmetry indicator to diagnose Weyl semimetal.We found that the mismatch between the symmetry indicator ? of S₄ and the time reversal symmetry indicator Z₂,namely ??Z₂,can be used to determine the existence of a Weyl point in the system.Based on this criterion,a series of copper-based chalcogenide compounds in stannite structure,which were considered topological insulators before,were examined.We found that some of the materials are actually Weyl semimetals satisfying ??Z₂.