The Study On The First-principles Calculations Of Topological States

In Landau-Ginzburg’s theory,systems can be classified very much according to their symmetries.In the process of phase transition,the symmetry of the system will be broken.The discovery of quantum Hall effect goes beyond Landau’s theory of sponta-neous symmetry breaking.The ensuing topological states of matter has led to a wave of research into new materials.At the same time,the development of computer technol-ogy and the maturation of computational physics have allowed more and more scientific problems to be solved by means of computational simulations.The first-principles cal-culations play a huge role in the field of condensed matter physics,especially in the study of topological states,where a large number of topological materials are first dis-covered by calculations and then experimentally confirmed.This is of course due to the stability of topological states to perturbations,which has made first-principles cal-culations a great success in this field.In this paper,I first review the development of the topological state and the first principles calculation theory and method.In the third and fourth chapters,I introduce my two research works on topological states.The last chapter is the summary and prospect of my work during my Ph.D.career.In Chapter 3,motivated by the discovery of ferromagnetic van der Waals layered metal-organic framework Cr Cl₂（pyrazine）₂,we theoretically propose that the single layer of Cr Cl₂（pyrazine）₂might realize one or some of these interaction driven states based on the quadratic band crossing points（QBCP）protected by₄symmetry.The quadratic band crossing points at Fermi level in two-dimension have been proposed to be unstable under electron-electron interaction.The possible interaction driven states include quantum anomalous Hall（QAH）state and various nematic ordered states.In this work,By introducing the short-range density-density type repulsion interactions into this system,we have found the phase diagram depending on different interaction range and strength.The exotic phases include the staggered chiral flux state manifesting quantum anomalous Hall effect,the site-nematic insulator and the site-nematic Dirac semimetal state.The quantum anomalous Hall state is robust against perturbations breaking the QBCP but it is weakened by increasing temperature.The metal-organic framework is tunable by changing the transition-metal elements,which might improve the gap size and stability of this interaction induced QAH state.In Chapter 4,we reported the structure and properties of ATi₃Bi₅（A=Rb,Cs）family with a Ti-Kagome lattice,specifically focusing on the electronic structure and nontrivial band topology of Rb Ti₃Bi₅.ATi₃Bi₅（A=Rb,Cs）is found to be non-superconducting metal with strong quasi-two-dimensional feature and small Pauli para-magnetism.Based on first-principles calculations,Rb Ti₃Bi₅is determined to be a weak topological insulator with gapless surface states along（100）plane,and the electronic band structure along（001）plane is in great agreement with experimentally observed one.In particular,the electronic properties of the Rb Ti₃Bi₅monolayer can be efficiently tuned by a biaxial strain according to calculation,with its lower saddle points coming from Kagome lattice approaching the Fermi level.These results highlight ATi₃Bi₅（A=Rb,Cs）with Ti-Kagome lattice is a new Kagome metal to explore nontrivial band topology and exotic phases.