Quantum Transport In Topological Superconductors And Non-Hermitian Systems

In the past ten years,the exploration of the topological properties has become the hottest research direction in the field of condensed matter.Like traditional insulators,an insulating band gap exists in the topological materials.However,there are edge states that can conduct electrons at the boundary of two-dimensional topological materials.This topologically protected edge state is robust and is naturally immune to disorder in the system.In the Hermitian system,the number and the direction of transport of edge states are determined by the topological invariants described by the Hamiltonian of their bulk states.This property is called the body-boundary state correspondence.Through quantum transport signals,this edge state that is not scattered by impurities can be accurately observed.Today,topological phases have been widely extended to other branches of condensed matter physics,such as: topological superconductors,topological quantum computing,topological optics and nonHermitian systems,etc.In this thesis,we use the method of non-equilibrium Green's function to explore the quantum transport properties of topological superconductors,non-Hermitian quantum rings and the extended Kitaev model.(1)We numerically investigate the electronic transport properties(i.e.,electron tunneling and Andreev reflection)of a topological superconductor composed of a magnetic topological insulator and superconductors.A phase diagram is provided to distinguish various topological phases and their corresponding distinct Majorana edge modes.When superconductors are proximity coupled with the top and bottom surfaces of a magnetic topological insulator thin film,a quantum phase transition from topological insulator to quantum anomalous Hall effect passes through the regime possessing both chiral and helical edge modes.The hallmark feature is that the coefficient of electron tunneling is quantized to be 5/4 and the remaining scattering processes exhibit an identical probability with a magnitude of 1/4 in the coexisting states with a Chern number of N = ±1.When the superconductors are proximity coupled with a nonmagnetic topological insulator thin film,we find that the perfectly quantized electron tunneling or crossed Andreev reflection can alternately appear via tuning the chemical potential;(2)We investigate the topological properties,energy spectrum,and persistent currents of a non-Hermitian ring with anti-Hermitian hopping terms.It is demonstrated that the antiHermitian hopping can effectively induce a synthetic gauge field.As the magnetic flux of the synthetic gauge field threads through the ring,the non-Hermitian system exhibits an Aharonov-Bohm effect.For the case of a non-Hermitian ring in the topological phase,the system,having an energy spectrum structure with a real gap,supports an imaginary persistent current.For the trivial case,a non-Hermitian system with an imaginary gap supports a real persistent current.Furthermore,we also investigate the transport property of a non-Hermitian Aharonov-Bohm ring connected by two semi-infinite leads.We find that the transmission coefficient shows the Aharonov-Bohm quantum oscillation as a function of the synthetic gauge field;(3)We propose a non-Hermitian extend Kitaev model with the anti-Hermitian hopping terms between the electron and hole where the chain holds the non-Hermitian skin effect.There are two topological phases in non-Hermitian Kiteav chain which is defined by the winding number.For the topological trivial phase,the Kitaev chain possesses purely real eigenvalue spectra protected by the PT-symmetry and all bulk states localized at the one end of the chain.In the topological nontrivial phase,the Kitaev chain,going through a PT-symmetry breaking transition,holds the Majorana zero-energy modes and the non-Hermitian skin modes at the end of the chain.We propose a quantum transport method to detect the skin modes and the zero-energy edge modes in one-dimensional topological chain.The electronic tunneling can probe the amplified skin modes at the end of non-Hermitian chain and the Andreev reflection can provide the transmission signal of the Majorana zero-energy modes;...