Predictions Of Novel Topological Materials From First-princples Calculations

In the past decade,the research of topological electronic materials has gradually become a hot topic in the field of condensed matter physics.Topological insulators,topological crystal insulators,topological superconductors,and various topological semimetals are included.The topological quantum states of these topological materials are protected by various symmetries,so one of their very important features is topological robust.The nature is not affected by the external environment perturbation,which is the advantage of the topological materials for the potential applications in spintronics and topological quantum computing in the future.In recent years,theoretical analysis,computational predictions and experimental progress of topological materials have yielded fruitful results.Among them,first-principles calculations based on density functional theory play an important role in this,and more and more new topological materials are predicted and then verified by subsequent experiments.In a series of works of this dissertation,we used first-principles calculations to predict several new topological materials.These new topological materials may provide guidance and direction for experiments.The specific content of this dissertation is arranged as the following:In the first chapter,we introduce the development history of topological phases,from quantum Hall effect to topological insulators to topological semimetals.We focus on the symmetry and topological properties of topological semimetals,including Dirac semimetals,Weyl semimetals,and nodal line semimetals.In the second chapter,we introduce the first principles calculations on density func-tionals,the Wannier function and the k·p model.In the third chapter,we theoretically predict the quantum spin Hall effect?QSHE?in the hydrofluorinated bismuth?Bi₂HF?nanosheet where the hydrogen?H?and fluorine?F?atoms are functionalized on opposite sides of bismuth?Bi?atomic monolayer.Such Bi₂HF nanosheet is found to be a two-dimensional?2D?topological insulator with a giant band gap of 0.97 eV which might host room temperature QSHE.The atomistic structure of Bi₂HF nanosheet is noncentrosymmetric and the spontaneous polarization arises from the hydrofluorinated morphology.The phonon spectrum and ab initio molecular dynamic?AIMD?calculations reveal that the proposed Bi₂HF nanosheet is dynamically and thermally stable.The inversion symmetry breaking together with spin-orbit coupling?SOC?leads to the coupling between spin and valley in Bi₂HF nanosheet.The emerging valley-dependent properties and the interplay between intrinsic dipole and SOC are investigated using first-principles calculations combined with an effective Hamiltonian model.The topological invariant of the Bi2HF nanosheet is confirmed by using Wilson loop method and the calcu-lated helical metallic edge states are shown to host QSHE.The Bi₂HF nanosheet is therefore a promising platform to realize room temperature QSHE and valley spintronics.In the fourth chapter,using first principles calculations,we predict a new 2D carbon allotrope,namely penta-octa-graphene,which consists of pentagonal and octagonal carbon rings.We find that penta-octa-graphene can host both type-I and type-II Dirac line nodes?DLNs?.The band inversion between conduction and valence bands forms the type-I DLNs and the two highest valence bands form the type-II DLNs.Moreover,the type-I DLNs are robust to the biaxial strain and the type-II DLNs is driven to type-I when applying over 3%biaxial stretching strain.A lattice model based on the orbitals of carbons is derived to understand the coexistence mechanism of type-I and type-II DLNs in penta-octa-graphene.In addition,we study the topological edge states from the projected type-I and type-II DLNs.Possible realizations and characterizations of this penta-octa-graphene in the experiment are also discussed.Our findings shed new light on the study of coexistence of multiple topological states in the 2D graphene allotropes.In the fifth chapter,we propose that the noncentrosymmetric LiGaGe-type hexagonal ABC crystal SrHgPb realizes a new type of topological semimetal that hosts both Dirac and Weyl points in momentum space.The symmetry-protected Dirac points arise due to a band inversion and are located on the sixfold rotation z-axis,whereas the six pairs of Weyl points related by sixfold symmetry are located on the perpendicular k_z=0 plane.By studying the electronic structure as a function of the buckling of the HgPb layer,which is the origin of inversion symmetry breaking,we establish that the coexistence of Dirac and Weyl fermions defines a phase separating two topologically distinct Dirac semimetals.We formalize our first-principles calculations by deriving and studying a low-energy model Hamiltonian describing the Dirac-Weyl semimetal phase.We conclude by proposing several other materials in the non-centrosymmetric ABC material class,in particular SrHgSn and CaHgSn,as candidates for realizing the Dirac-Weyl semimetal.In the last chapter,we make a brief summary of the full text,and give some future prospects of first-principles prediction of topological materials.