Theoretical Study Of The Impurity Scattering Effect In Topological Systems

Topological insulators(TIs),characterized by the topologically protected gapless boundary states,have enjoyed a surge of research interest in condensed-matter physics.The gapless boundary states inside the bulk band gap distinguish the TIs from ordinary insulators,adiabatically.The boundary states are protected by the time-reversal(TR)symmetry,and the spins of electrons are locked to their momenta in a helical or chiral structure.As a consequence,the gapless boundary states are robust to TR invariant per?turbations,and perfect backscattering from TR invariant impurities is prohibited.The unique topological properties make TIs promising materials for applications in spin-tronics and topological quantum computation.Based on the Green's function method and linear response theory,we study the impurity scattering effects of topological sys-tems theoretically in this dissertation.The dissertation consists of six chapters:Chapter one is an introduction,in which we briefly introduce the development and properties of the TIs.In section four of this chapter,we derive the Kubo-Streda formula in a new way,and generalize it to the case of finite frequency.In chapter two,the interaction effect between the surface states of a TI and a STM-coupled Anderson impurity is studied by using equations of motion of the Green's functions.Remarkably,we show that when a coupling between the Anderson impurity and the STM tip is included,the tunneling resonance and the Kondo peak can be tuned to be exactly at the Dirac point,by adjusting the impurity level and Fermi energy,such that the local density of states at the Dirac point is significantly enhanced.This is in contrast to the case of a STM-decoupled Anderson impurity,where both resonances are always fully suppressed at the Dirac point.Our finding suggests a pathway to experimentally control the fundamental properties of the electrons on a TI surface.In chapter three,we consider the Dirac electron scattering off a pointlike impurity absorbed on the surface of a TI,which is irradiated by a beam of circularly polarized light.It is found that the Dirac electron backscattering is allowed even for a nonmag-netic impurity due to the reshuffled spectrum caused by the light,and so exhibits inter-esting spin texture and Friedel oscillation in the real space.Furthermore,in the charge density of states,the interplay of the light irradiation and impurity scattering can lead to an in-gap bound state around the Dirac point,heavily modulating the Dirac dispersion.We discuss the different scenarios for resonant and off-resonant lights in detail.The impurity scattering feature is sensitive to the parameters of the polarized light,which suggests a possibility to optically manipulate the topological surface states.In chapter four,we investigate the anomalous Hall effect(AHE)on the surface of a topological insulator induced by a finite concentration of magnetic impurities,and find topologically nontrivial and trivial mechanisms simultaneously contributing to the Hall conductivity.In the topologically nontrivial mechanism,the impurities gap the surface spectrum and result in a half-integer quantized intrinsic Hall conductivity in units e2/h,while in the topologically trivial mechanism,the half-integer quantized plateau is mod-ified by impurity-induced localized states via a gap-filling process.The nonmagnetic charge potential itself,though participating in the gap-filling process,cannot induce the AHE.In the presence of a finite magnetic potential,the charge potential would destroy the symmetric distribution of the Hall conductivity by redistributing the localized lev-els.More interestingly,the sign of the Hall conductivity is tunable by changing the strength of the charge potential.In chapter five,we theoretically study the effect of impurity scattering in a magnet-ically doped Dirac semimetal.It is found that the magnetic impurity potential can split a Dirac point into a pair of Weyl nodes,due to the broken time-reversal symmetry,and the DSM undergoes a topological phase transition to a Weyl semimetal(WSM).The Chern numbers on a cross section between the Weyl nodes in the Brillouin zone are integer quantized.As a consequence,open Fermi arcs emerge,which connect the pro-jections of the Weyl nodes on the surface Brillouin zone.However,a relatively strong magnetic potential,in addition to separating the Weyl nodes,will introduce some lo-calized states to the system.These localized states smear the Weyl nodes,and the anomalous Hall conductivity deviates from the linear dependence on the momentum distance of the Weyl nodes.Interestingly,though the nonmagnetic charge potential of the impurities is shown to be irrelevant to the topological phase transition,it can mod-ify the Berry curvature and anomalous Hall conductivity of the impurity-induced WSM phase,by redistribution of the energies of the localized states.The last chapter contains a summary of this dissertation,and we also give some outlook for the further investigation...