Disorder Effect And Transport Properties Of Low-dimensional Topological System

Topological states have unique transport characteristics.Considering that disorder inevitably exists in real systems,it is very important to study the response of topological states to disorder and the related transport properties.In particular,it is of great significance to study how to realize and manipulate dissipationless transport channels by external methods to meet the requirement of future electronic devices with low power consumption.In addition,topological states in non-Hermitian systems have recently become the research frontier.As a unique non-Hermitian topological effect,the nonHermitian skin effect induced by the point-gap topology has been widely concerned.The study on the response of non-Hermitian skin effect to disorder is not only helpful to understand the topological properties of non-Hermitian systems,but also the basis for further study of quantum transport.This thesis investigates the disorder effect and transport characteristics of three topological states,which mainly contains the following three parts:(1)We have studied the transport properties of states on the graphene under pseudomagnetic fields(PMF)induced by inhomogeneous strain and disorder.We find that both edge states and pseudo-Landau level(PLL)states induced by the PMF can act as onedimensional conducting channels.However,all of these states are fragile to disorder.We further demonstrate that the spatial distribution of PLL channels is energy-dependent,so the backscattering of different PLL channels can be adjusted by modulating the distribution of disorder.Furthermore,the backscattering for both edge channels and PLL channels under PMF can also be suppressed by an external magnetic field,which indicates that the disordered strain graphene system has the potential application as a switching device by manipulating the external magnetic field strength.(2)We have proposed a programmable integrated circuit with the help of disordered Chern insulators(CIs).On the one hand,we use the external-gate-induced step voltage to construct spatially tunable chiral interface channels in disordered CIs.These channels can be programmed via a gate voltage array to connect any required device.In particular,our numerical calculations manifest that the electron transport in the chiral interface channels is dissipationless and robust against gate voltage fluctuation and disorder strength.On the other hand,we have implemented all seven basic logic gates using the programmability of the chiral interface channel.Compared with the traditional logic gates,these disorderedCIs-based logic gates have no power consumption and their structures are greatly simplified.Our proposed programmable wires and logic gates based on the CIs provide a new way for the realization of the integrated circuits in topological systems.(3)We have studied the influence of Anderson disorder on non-Hermitian skin effect(NHSE)under different dimensions.Based on the summation of the eigenvectors,we define a physical quantity p to characterize the existence and direction of the non-Hermitic skin effect.For one-dimensional systems,we demonstrate the existence of mobility gap for NHSE under disorder,and this mobility gap can be characterized by p,which separates states with and without NHSE.Furthermore,we establish a method to obtain p under the thermal dynamic limit.For two-dimensional systems,we show that p is efficient to characterize the direction of NHSE,and the stability of NHSE is independent of the direction of NHSE.Importantly,by comparing one-dimensional and two-dimensional disordered systems,we find that the increase of dimension can significantly enhance the robustness of NHSE to disorder.