Topological Related Physics In Free-fermion Condensed Matter Systems

Recent years have witness the rapid development of the research on topological and symmetry-protected topological states of condensed matter systems.In this thesis,we study some examples of the topological states,and predict several new materials to realize those novel states with theoretical model.We mainly focus on the following three topics.First,on the basis of first-principles calculations and an analytical effective model,we propose a family of two-dimensional Dirac materials,such as(LaO)2(SbSe2)2.This material has eight Dirac cones,and the advantage lies in its tunability by an external electric gate voltage: the existence of gapless Dirac cones,their positions,Fermi velocities and anisotropy can be controlled by an experimentally feasible electric field.We identify layer-dependent spin texture induced by spin-orbit coupling as the underlying physical reason for electrical tunability of this system,and find that the Dirac cones are protected by mirror-reflection symmetry.Furthermore,the quantum anomalous Hall effect with a high Chern number may be realized by introducing magnetization into this system,and by changing the gate voltage the Chern number of system could be tuned from 4 to 0,and to-4.Next,we study another way to realize quantum anomalous Hall phases.We find that in an anti-ferromagnetic film of Sr2FeOsO6,the band inversion could be achieved by applying an external gate voltage and this will lead to a phase transition from trivial insulator to quantum anomalous Hall phase.Moreover,when the superconducting pairing terms are introduced by proximity effect with an s-wave superconductor,the chiral topological superconducting phases could be realized in this system.Finally,we investigate the three-dimensional topological crystalline insulators,and present a general theory to classify them.The three-dimensional systems with a surface are described by two-dimensional space group.Based on the relationship between the band degeneracy and symmetry,we find all the topological non-trivial surface states,give the corresponding topological invariants of the bulk and build some models to realize the non-trivial surface states explicitly.