| The nontrivial topological edge states have an important application in spintronics and quantum computing due to that being robust to the local defects and disorder of the materials.The Su-Schrieffer-Heeger(SSH)chain originally introduced for describing the polyacetylene is the simplest one-dimensional model with the nontrivial topological edge states,which has been experimentally realized in the photon,cold atom and engineered atomic systems.In order to realize quantum devices based on the nontrivial topological edge states,how to detect the nontrivial topological edge states is one of the important topics in condensed matter physics.In this thesis,we will study the relationship between the nontrivial topological edge states and the electron transport properties of the two systems,namely,the SSH chain with the spin-orbit coupling and the non-Hermitian SSH chain with the anti-Hermitian intra-cell hopping,and explores a theoretical scheme of detecting the nontrivial topological edge states depended on the electron transport properties.(1)In the SSH chain,the nontrivial topological edge states will have different winding numbers when the intra-cell and inter-cell hopping amplitudes are spin-dependent ones.It is demonstrated that the winding numbers of the quadruple-degenerate and twofold-degenerate edge states are two and one,respectively.Importantly,the electron transport properties in the vicinity of the zero energy can characterize the energy spectrum of the edge states,when the spin-polarized electrons tunnel into the SSH chain from the source lead,namely,the source lead is a ferromagnetic one.In particular,with increasing the tunneling coupling strengths between the SSH chain and the two leads from the weak coupling regime to the strong coupling one,the number of transmission resonance peaks of the quadruple-degenerate with the winding numbers being two and twofold-degenerate edge states with the winding numbers being one will be reduced by four and two,respectively.In other words,the transmission resonance peaks related to the edge states will disappear when the SSH chain is strongly coupled to the two leads.Therefore,these results suggest that an alternative way of detecting the nontrivial topological ones with different winding numbers by the variation of the number of transmission resonance peaks of edge states.Furthermore,the nontrivial topological edge states of the SSH chain with the spin-orbit coupling and the detection scheme of nontrivial topological edge states mentioned above are both robust to the non-diagonal disorder(namely,the hopping amplitude disorder).(2)The non-Hermitian SSH chain with the anti-Hermitian intra-cell hopping does not have the skin effect,and the traditional bulk-boundary correspondence is still valid.Therefore,the Bloch winding numbers,the non-Bloch winding numbers and the state-dependent topological invariants can be used to characterize the topological properties of the non-Hermitian SSH chain.It is demonstrated that the non-Hermitian SSH chain has a pair of nontrivial topological edge states.In particular,when the non-Hermitian SSH chain has the nontrivial topological edge states,with increasing the tunneling coupling strengths between the non-Hermitian SSH chain and the source and drain leads from the weak coupling regime to the strong coupling one,the number of transmission resonance peaks in the vicinity of the zero energy will vary from two to zero.Therefore,by modulating the tunneling coupling strengths between the non-Hermitian SSH chain and the source and drain leads,we can observe the variation of the number of transmission resonance peaks in the vicinity of the zero energy to detect whether the non-Hermitian SSH chain has the nontrivial topological edge states or not. |
