Topological Phase Transitions And Transport Properties In Low Dimensional Topological Systems

Topological insulators and their extensions of symmetry protected topological s-tates are currently on the research front of condensed matter physics,because of their fundamental interest and potential applications in spintronic devices.The non-trivial bulk topological properties can result in the novel physical properties,such as the edge states.These properties are insensitive to smooth changes in material parameters,and robust to impurities and weak disorder.In this thesis,we mainly study topological phase transitions and transport properties in the low dimensional topological systems,included the non-adiabatic topological spin pumping,Zeeman-field-tuned topological phase transitions in a two-dimensional Class-D? superconductor,? spin Berry phase induced by the helical edge states,and the AC quantum spin Hall(QSH)effect.In chapter two,based on the Floquet scattering theory,we analytically investi-gate the topological spin pumping for an exactly solvable model.Floquet spin Chem numbers are introduced to characterize the periodically time-dependent system.It is a generalization of the spin Chern number that was previously introduced in the adiabat-ic limit to any periodically driven one-dimensional fermionic systems.The topological spin pumping remains robust both in the presence and in the absence of the time-reversal symmetry,as long as the pumping frequency is smaller than the band gap,where the electron transport involves only the Floquet evanescent modes in the pump.For the pumping frequency greater than the band gap,where the propagating modes in the pump participate in the electron transport,the spin pumping rate decays rapidly,marking the end of the topological pumping regime.In chapter three,we investigate the topological phase transitions in a two-dimensional time-reversal invariant topological superconductor in the presence of a Zeeman field.Based on the spin Chern number theory,we find that the system exhibits a number of topologically distinct phases with changing the out-of-plane component of the Zeeman field,including a quantum spin Hall-like phase,quantum anomalous Hall-like phases with total Chern number C =-2,-1,1 and 2,and a topologically trivial supercon-ductor phase.The BdG band gap closes at each boundary of the phase transitions.It is revealed that the nontrivial topological properties of the bulk wavefunctions remain robust against magnetic disorder.The BdG energy and spin spectra of the edge states calculated for a nanoribbon are consistent with the topological characterization using the spin Chem numbers.Furthermore,the basic characteristics of the zero bias conduc-tance are investigated,which can be used to identify the different topological phases experimentally.In chapter four,we investigate the coherent edge-state transport in an interference loop pinched by two point contacts.Although the edge-state conduction in the QSH system has been observed,unambiguous evidence of the helical spin texture is still lacking.Due to the helical character,the forward inter-edge scattering enforces a ? spin rotation.Two successive processes can only produce a nontrivial 2? or trivial 0 spin rotation,which can be controlled by the Rashba spin-orbit coupling.The nontrivial spin rotation results in a geometric ? Berry phase,which can be detected by a ? phase shift of the conductance oscillation relative to the trivial case.Our results provide a smoking gun evidence for the helical spin texture of the edge states.Moreover,it also provides the opportunity to all-electrically explore the trajectory-dependent spin Berry phase in condensed matter.In chapter five,we investigate that a QSH system behaves quite differently in re-sponse to an applied AC electric field,and propose the idea of AC QSH effect.In the DC regime,the transport in QSH system relies on the existence of symmetry-protected edge states.However,based on the Kubo linear response theory,we find the AC QSH effect can occur in the bulk without involving the fragile edge states,hence being ro-bust against time-reversal symmetry breaking and disorder.Then,we develop an an-alytical theory of the low-frequency AC QSH effect based upon the scattering matrix formalism.It is shown that the AC QSH effect can be interpreted as a bulk quantum pumping effect.When the electron spin is conserved,the integer-quantized AC spin Hall conductivity can be linked to the winding numbers of the reflection matrices in the electrodes,which also equal to the bulk spin Chem numbers of the QSH material.Fur-thermore,a possible experimental scheme by using ferromagnetic metals as electrodes is proposed to detect the topological AC spin current by electrical means.