Theoretical Studies On Transport And Modulation Of Topological States

To explain the phase transitions without symmetry-breaking,physicists have intro-duced topology into condensed matter physics.According to the topological invariants in mathematics,the topological phases of matter can be classified.With the develop-ment of modern computer science,the first-principles calculations effectively predict the topological properties of materials.Under the guidance of theoretical calculations,the field of topological materials has grown rapidly to become a research hotspot in condensed matter physics.In recent years,both theoretical and experimental researches have discovered several topological materials with novel physical properties.By study-ing the modulation of topological states,this thesis puts forward new ideas and methods for applying topological materials.In Chapter 1,we introduce the theoretical methods used in the research.We firstly introduce the first-principles calculation based on density functional theory.In peri-odic systems,the theoretical basis and the calculation framework are further explained.In addition,combining the tight-binding model and the surface Green’s function,we introduce the calculation method of surface spectrum.Finally,we briefly review the software packages.In Chapter 2,we introduce the properties of topological materials.According to the electronic structure,we divide the topological materials into two categories:insulators and semi-metals.For topological insulators,we concentrate on the quantum Hall effects in two-dimensional systems.Moreover,we discuss the calculation methods of topolog-ical invariants.For topological semi-metals,we mainly introduce the Dirac fermion and the Weyl fermion.Based on the chiral anomaly of Weyl fermion,we focus on the topological transport.In Chapter 3,we investigate the modulation of folded graphene with light irradia-tion.The circularly polarized light can gap graphene systems,and realize the quantum anomaly Hall effect.By folding graphene,we create a type-II topological interface with one-light setup.With the studies on carbon nanotubes,we prove the stability of light-induced topological states and the generality of modulation with light irradiation.To realize three-dimensional light-induced Chern insulators,we further study the folding modulation of topological states.In this chapter,combining two modulation methods,we expand the research methods of two-dimensional topological materials.In Chapter 4,we study the Te elementary system doped with vacancies.In the transport experiment of Te elemental samples,our experimental collavorators have dis-covered a series of topological transport phenomena.In order to explain these phe-nomena,we study the origin of carriers in samples and the topological properties of Te.The Fermi level of vacancy model is located in the valence bands,which proves that the holes result from Te vacancies.In addition,by analyzing the spatial distribution of impurity energy levels,we find that the defects form negative charge centers.In the vacancy bands of Te,we prove the existence of Weyl fermions.In the experiment,the chiral anomaly leads to the transport phenomena.Combining with the experimental results,we explain the log-periodic quantum oscillations in Te.In Chapter 5,we realize a second-order topological insulator in the monolayer FeSe by adjusting the magnetic moments.According to the monolayer FeSe,we study the relation between topological corner states and magnetic moments with two methods.On the one hand,based on the effective Hamiltonian,we demonstrate the fractional mass-kinks can induce topological corner states.On the other hand,using the first-principles calculation,we study the FeSe cluster with tilted magnetic moments.The existence of topological corner states are directly verified.