Topological Properties Of 2D Iron Chalcogenides Studied By First-principles Calculations

As a new quantum state,topological state has many novel properties.For example,topological insulator is a novel material characterized by the non-trivial topological order.It behaves as an insulator in bulk state,while possesses a gapless and Dirac-type metallic surface state in which spin and momentum are locked.Moreover,their topological invariant number is not sensitive to defects.Such robustness provides various application possibilities.Besides topological insulators,more novel states such as topological semimetals and topological superconductors have been predicted and discovered.In this thesis,the topological properties and their effects on physical properties of 2D FeSe,an iron-based superconducting material,are studied from the perspective of electronic structure.In the first chapter,the development of topological states is introduced,and the concepts of quantum Hall effect,quantum anomalous Hall effect,quantum spin Hall effect,topological invariants and topological superconductor are given.The second chapter introduces the foundation of density functional theory and the concept of Wannier function.Next in the third chapter,by using the First-principles calculations and theoretical analysis,we've studied the electronic structure and topological properties of 2D FeSe in detail.We have calculated the electronic structures of monolayer FeSe with nonmagnetic,checkerboard antiferromagnetic,collinear antiferromagnetic and bicollinear antiferromagnetic order respectively.By comparing the electronic structure with the experimental results,we find that the checkerboard antiferromagnetic order fits the experimental results best and take it as the typical case.Then we construct the Maximally localized Wannier functions near the Fermi level based on the 3d orbitals of Fe and the 4p orbitals of Se.Then the tight-binding(TB)Hamiltonians of semi-infinite sample are also constructed and used to calculate the edge states iteratively.Base on the symmetry analysis,we point out that the spin Chern number of the system is 1,which has gapless edge states only at certain boundary.And we have calculated the energy evolution of 3d orbitals versus lattice constance a and so does the bilayer.The topological properties and the edge states in the AFM bilayer FeSe are also studied,and the results perfectly explain the characteristic peaks and other phenomena observed in the experiment.In the fourth chapter,we further study the topological phase transition caused by Te atom doping and unidirectional lattice distortion quantitatively.The range of parameters that maintain the topological insulating phase is given at both computational and model level,which shows that lattice distortion can reduce the dependence of topological phase transition on Te doping.What's more,the unidirectional lattice distortion leads to C4 symmetry breaking and makes the edge states different between x and y direction,which makes it possible to obtain Majorana corner states in superconducting phase.Further calculations and model analysis support the Majorana corner states in rectangular FeSexTe1-x/SrTiO₃.