| The discovery of the topological properties of materials is an important progress in the process of our understanding of the material world.Topological materials have topologically protected edge states and exhibit many novel quantum properties which have received extensive attention in the field of condensed matter physics.Exploring materials with novel topological characteristics and investigating their properties constitutes a crucial research directions in the field of topological materials.The topological materials can be divided into first-order topological insulators and higher-order topological insulators according to the dimensional difference between topological state and bulk state.First-order topological insulator,whose topological state is one dimension lower than the bulk state,includes Z2 topological state,quantum anomalous Hall effect,etc.High-order topological insulator is a class of topological insulators whose dimension difference between the bulk state and topological state is greater than or equal to two.For instance,the topological state of a threedimensional second-order topological insulator is the hinge state.Though the dimensions are different,the formation mechanism and corresponding properties of first-order topological insulator and higher-order topological insulator have similarities.This thesis mainly focuses on quantum anomalous Hall effect and high-order topological states:predicted several valley-polarized quantum anomalous Hall material systems and twodimensional second-order topological insulators;studied the topological properties of hinge states in three-dimensional second-order topological insulators;studied the homogeneity of magnetically doped topological insulator thin films and its thickness-driven quantum anomalous Hall phase transition.These studies reveal that both first-order and higher-order topological states exhibit remarkable robustness.Furthermore,magnetism plays a significant role in the formation of these topological states.The first chapter introduces the basic concepts,models and materials of topological states,and describes the application of circular photogalvanic effect(CPGE)in detecting geometric properties.Two one-dimensional topological models:SSH model and Jackiw-Rebbi model are introduced to illustrate the concept of topology.Furthermore,we introduce the topological states in two-dimensional systems which are focused on in this thesis,including quantum anomalous Hall effect,Z2 topological insulator and quantum valley Hall effect.These topological states are characterized by their bulk insulating properties and edge conductivity.Next,the higher-order topological insulators are introduced from the perspective of dimensions and the theoretical models.The topological states of higher-order topological insulators share very similar properties with those of first-order topological states.This chapter also contains the physical process of the CPGE and its application in detecting the topological properties of materials.The second chapter introduces the theoretical foundations and basic research methods involved in this thesis.We mainly discuss two numerical methods for calculating the Berry curvature,the tight-binding model method,and the first-principles calculation method.To describe the energy spectrum and topological properties of a system,we typically construct its Hamiltonian using either the tight-binding model method or the first-principles calculation method.Once the Hamiltonian is obtained,we can use numerical methods to calculate the Berry curvature and describe the system’s topological properties.In Chapter 3,we predict a valley-polarized quantum anomalous Hall effect material,and further explore its potential application as a valleytronic device to modulate the valley,spin,and layer degrees of freedom.We find that introducing an A/B unequal magnetic exchange field into a hexagonal lattice system with strong intrinsic spin-orbit coupling can achieve valley polarization.When the exchange field makes the valence band and the conduction band cross in a valley and further open a band gap,one realize the valley-polarized quantum anomalous Hall effect.Using the first-principles calculation,we found that the Pt2HgSe3/CrI3 heterostructure satisfies our consideration of the above low-energy effective model.The calculation results show that it can open a topological band gap of 17.8 meV and realize a valley polarization of 136.3 meV.We further use the h-BN/Pt2HgSe3/CrI3 hetero structure as a building block to make a device.By changing the stacking orders and magnetization directions,one can control the spin,valley,and layer degrees of freedom.Our findings provide an ideal platform for studying the quantum valley Hall effect and quantum anomalous Hall effect.Our findings provide an ideal platform for studying the quantum valley Hall effect and quantum anomalous Hall effect.In Chapter 4,we theoretically predict the realization of second-order topological states in the heterostructure of Jacutingaite materials and two-dimensional magnetic materials.The physical mechanism and stability of the second-order topological corner state are further analyzed.By analysing the properties of MZ2/Pt2XY3/MZ2(M=Co and Ni;Z=Br and Cl;X=Zn and Hg;Y=S and Se),we find four heterostructures with gapped edge states and topological corner states.We link the two-dimensional secondorder topological state with a one-dimensional Jackiw-Rebbi model,which can explaine the existence of the topological corner states.Furthermore,we discover that applying additional onsite potentials at the boundary,constructing irregular boundaries,or introducing Anderson disorder does not destroy the topological corner states.This suggests that second-order topological insulators are highly robust.In Chapter 5,we demonstrate that the topological hinge state can possess a nontrivial optical Berry curvature in the nonAbelian formulation of the Berry curvature.It can be readily probed by the CPGE,with the light illuminating a specific hinge,and we refer to it as the hinge CPGE.As a concrete example,we calculate the hinge CPGE in ferromagnetic MnBi2nTe3n+1,and find that the hinge CPGE peak structure well reflects the optical Berry curvature of hinge states and the optical sum rule captures the optical Berry curvature between the hinge state and the ground state.The hinge CPGE provides a promising route towards the optical detection of the hinge state geometrical structure.In Chapter 6,we study the homogeneity of magnetically doped topological insulator and its thickness-driven quantum anomalous Hall phase transition.By calculating the mixing energy of the magnetically doped topological insulator,we investigate the magnetic homogeneity of Cr-and V-doped Bi2Se3,Sb2Te3 and(Bi,Sb)2Te3,and study the mixing uniformity of Bi and Sb in the experimental system(Bi,Sb)2Te3.We find that the inhomogeneous mixing of Bi and Sb in the experimental system(Bi,Sb)2Te3 is the reason for the inhomogeneous magnetic doping.Furthermore,through model analyses and first-principles calculations,we find that there are two aspects causing the thickness-driven quantum anomalous Hall phase transition in Cr-doped(Bi,Sb)2Te3:first,the decrease of the film thickness enlarges the hybridization gap,making it much more difficult to achieve quantum anomalous Hall effect;second,the decrease of the film thickness also weakens the intrinsic magnetic exchange coupling of the magnetic topological insulators.In Chapter 7,we summarize all the work in the thesis and provide future directions for further exploration. |
