Disorder Effect And Transport Properties Of Topological Systems

With the development of topological theory,many topological states are proposed in theory and realized in experiments.The Chern insulator(CI)is one of the most focused.The study on enhancing the energy window with quantized transport using external methods other than by enhancing the spin-orbit coupling strength also attracted significant interest.Excepting for the CI,physicists recently paid great attention to the higher-order topological states and the non-Hermitian topological phases.The investigations of disorder effect on these topological states and their transport properties are urgently needed for uncovering their topological features.In this thesis,we study the disorder effect and the transport properties of above topological states.The main results are summarized as follows:(1).Since the CI belongs to the unitary ensemble,the disordered CIs host some discrete phase transition points with the bulk states localized for the entire energy region.We propose a setup,which combines the potential steps with the disordered CIs.Such a setup possesses the topological chiral-interface-states.The chiral-interface-states are protected by the integer Chern number difference between the potential step’s two sides.With the interface states’ help,we find that the energy window with quantized transport can be greatly enhanced.Further,the enhanced energy window is insensitive to the parameters and is considered realizable in MnBi2Te4.(2).We study the disorder-induced phase transitions in two-dimensional(2D)magnetic higher-order topological insulators(HOTIs)by adopting the machine learning method and the real space topological invariant method.We show that the corner states of HOTIs are robust against disorder and obtain several specific phase transitions.(3).We propose a unique charge pumping process in 2D HOTIs.Such charge pumping process will not pass through the samples’ bulk due to the mass domain wall sitting at the edge of the sample.Further,the pumping current’s direction can be adjusted by the coupling strength between the leads and the HOTI.Such a pumping process can be considered as the signal of two-dimensional HOTIs in condensed matter.(4).Very recently,a new kind of topological semimetal with Weyl-nodes,which is named higher-order Weyl semimetal(HOWSM),gains special attention in both theory and experiment.The HOWSMs are predicted to possess the Fermi-arc surface states as well as the hinge states.In particular,the hinge states hold the quantized charge and the electric quadrupole moment.These features draw a clear distinction between HOWSMs and the traditional Weyl semimetals(WSMs).We study the disorder-induced phase transition of HOWSMs and the fate of the topological features of disordered HOWSMs.We obtain a global phase diagram.Specifically,a direct phase transition from a WSM to a HOWSM is obtained,distinguishing the disordered HOWSM from the traditional WSM.We also confirm the robustness of Weyl-nodes for HOWSMs.Nevertheless,the unique topological properties of HOWSMs show different behaviors:(ⅰ)the quantized quadrupole moment and the corresponding quantized charge of hinge states are fragile to weak disorder;(ⅱ)the hinge states show moderate stability,which enables the feasibility for experimental observation.(5).Finally,we extend the real space topological invariant of Hermitian systems(the Chern number and the quadrupole moment)into the non-Hermitian systems.We study the stability of the Chern number as well as the quadrupole moment,which are defined in real space in non-Hermitian samples.We present the disorder effect on corresponding non-Hermitian systems as well as the disorder-induced phase transitions.The related topological Anderson insulators are also obtained.We emphasize that the extension of the real space topological invariant captures three main features of non-Hermitian systems:the Biorthogonal basis,the definition of gaps in the complex plane,and the non-Hermitian skin effects.Notably,the influence of unique symmetries of non-Hermitian systems are also considered.