| Due to the discovery of topological insulators and its experimental realization,the study of the band topology of solid materials has become an important subject of mod-ern condensed matter physics.Unlike conventional band insulators,there may exist a single pair of gapless helical edge or surface states in the bulk gap,exhibiting quan-tized conductance in transport experiments,when the Fermi level locates within the bulk gap.And the band topology can be characterized by a topological invariant such as Chern number or Z2 index.In recent years,topological semimetals have gradually become an important research topics due to their experimental realization.The low-energy quasiparticle can be described by the Dirac equation or the Weyl equation,and its band touching point has a nontrivial topology.The theoretical investigation of these novel and interesting quantum phenomenon in these topological materials not only has the significance of basic physics research,but also provides theoretical insights for re-lated experiments and applications.In Chapter 1,we briefly introduce the concept of topological materials,the bulk-boundary correspondence in topological materials,and the method of determining the band topology and its physical reasons.Firstly,as an example,the Haldane model is adopted to calculate the Chern number.Then,the concept of the topologically protected edge state is introduced by using the mass domain model and the BHZ Hamiltonian.Fi-nally,we discuss the Z2 invariant in topological insulators with time reversed symmetry preserved,and present the numerical methods to calculate the Z2 invariant.In Chapter 2,several widely adopted theoretical methods for dealing with disor-der problem are summarized.Firstly,after briefly introducing the diagrammatic per-turbation theory,we take graphene as an example to discuss the self-consistent Born approximation approach,and calculate the conductivity correction from quantum inter-ference.Then,we turn to the renormalization group(RG)calculation,another power-ful analytical tool for dealing with disordered problems.Taking two-dimensional and three-dimensional Dirac particles as examples,we calculate the RG flow equation of the disordered system.Based on the solution of the flow equation,we will discuss how the physical quantities(i.e.conductivity,density of states and group velocity)will be renormalized by disorder effect,and compare these results with what obtained from the scaling function theory.In the first section of Chapter 3,we introduce one simple approach to realize a topological phase transition by introducing a spatial periodic potential.As an example,we examine the electronic structures of HgTe/CdTe quantum wells,and demonstrate that their band structures can be effectively manipulated by the periodic potential.At a critical potential,we find that a conventional band insulator undergoes a topological phase transition into a quantum spin Hall system,which is characterized by an abrupt change of the spin Chern number and emerging edge states.Our proposal provides an interesting way to dynamically turn on or off topologically protected edge states for application in switching devices.In the second section,we explore the adsorbate effect on the electronic properties of silicene.The calculated local density of states around the adsorbates clearly reveal that the induced localized states contain the band topology information,which can be used to distinguish whether the system is a topological insu-lator or not.We also examine the impact of randomly distributed adsorbates with a low concentration on the electronic structures and the transport properties of silicene,and find that the edge mode backscattering is significantly enhanced when the energies of the incoming modes from leads match that of the in-gap localized states.In the first section of Chapter 4,we determine accurately the quasiparticle and s-caling properties of disordered 3D Dirac semimetals surrounding the quantum critical point separating the Dirac semimetal and diffusive metal regimes,with all higher or-ders of disorder scatterings fully treated,by using the enabling computational approach(the Lanczos method in momentum space).The imaginary part of the quasiparticle self-energy obeys a common power law before,at,and after the quantum phase transi-tion,but the power law is nonuniversal,whose exponent is dependent on the disorder strength.More intriguingly,whereas a common power law is also found for the real part of the self-energy before and after the phase transition,a distinctly different be-havior is identified at the critical point,characterized by the existence of a nonanalytic logarithmic singularity.This nonanalytical correction serves as the very basis for the unusual power-law behaviors of the quasiparticles and many other physical properties surrounding the quantum critical point.The second section of Chapter 4,we explore the quasiparticle behaviors in dis-ordered graphene especially in the strong disorder limit.The self-energy function-s obey the power law behavior for the whole disorder regime.In the weak disorder limit and away from the Dirac point,our simulations give the consistent results with self-consistent Born approximation,while in the strong disorder limit,our simulation-s avoid the singularity around the low energy scale and give more reasonable results.Moreover,we can also obtain the reliable conductivity in the strong disorder limit by using our obtained self-energy function.It is worth noting that our developed Lanczos numerical method in momentum space can be generalized to discuss the quasiparticle behaviors in the strong scattering regime in various waves with linear dispersion.In this thesis,we study the effects of various modulations on the electronic struc-tures and transport properties of topological materials.Our theoretical simulations and findings not only deepen the understanding of the physical properties of topological ma-terials,but also provide theoretical insights for future related experimental observations and applications. |
