The First-principle Study Of Topological Insulators And Semimetals

In recent years,the research of topological electronic materials is a hot topic in condensed matter physics.Topological electronic materials refer to the materi-als with nontrivial topology in k-space.This kind of materials can be divided into topological insulators,topological semimetals and topological superconductors and so on.The most important characteristic of topological electronic material-s is the robustness against environmental perturbations,and this characteristic promises the applications in many fields.The first-principle calculation is very important in the research of topological materials.More and more topological materials are predicted in theory and confirmed in experiment.In this dissertation,we predict several topological materials by using the first-principle calculations and provide some useful guides to experiment.Firstly,we will introduce some theoretical knowledge and methods,including the first-principle calculations based on density functional theory,pseudopoten-tial theory,wannier function and k · p method.All the studies in this thesis are based on these theories.Secondly,we predict that the oxide material ZrSiO is a three-dimensional（3D）weak topological insulator and the single layer is a 2D oxide topological insulator.We also find that the isostructural compounds WHM（W:Zr,Hf or La;H:group IV or V;M:group VI）have similar electronic structure.2D topological insulator ZrSiO forms a nodal line structure in mirror plane when we do not consider the spin-orbit coupling（SOC）effect,and a global gap near 30 meV will be achieved when we consider SOC effect.According to the band projection,we find that the band inversion is formed by the dx2-y2 orbits of Zr and px+py orbits of Si,and it is protected by the glide mirror symmetry.More-over,we also confirm the nontrivial topology of another isostructural compound ZrSnTe with experimental group by using angle resolved photoemission spec-troscopy（ARPES）and the first-principle calculations.This family of materials is worth to be studied.Thirdly,we also predict that CaP₃ is a topological nodal-line semimetal when we do not consider the small SOC effect.This material only has time reversal symmetry and space inversion symmetry,so it will forms a nodal line structure when these two symmetries are not destroyed.We also get the drumheadlike surface state on（001）surface,which is one of the most important characteristics of topological nodal-line semimetal.At the same time,we establish a two bands k · p model to confirm it.If we take the small SOC effect into consideration,we can find that the nodal-line will open a gap and it will becomes strong topological insulator.In the end,we make a simple conclusion of this paper.We also propose an efficient method,like high throughput searching method,to discover topological electronic materials.Depending on the materials library and the parameters of topological materials,the high throughput searching method greatly raises the efficiency of topological materials search.Meanwhile,it will open up a new prospect for the development of topological materials.