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The differential conductance tunnel spectroscopy in an analytical solvable two-terminal Majorana device

In this paper, we investigate the non-Markovian quantum transport dynamics of a two-terminal Majorana device that is made of an asymmetric topological superconducting chain coupled to two leads. This asymmetric superconducting chain is analytically solvable and can be realized by a hybrid system of semiconductor nanowire coupled to superconductors or by 1D transverse-field Ising chains. In such asymmetric superconducting chains, by the change of chemical potential, its ground state undergoes a topological quantum phase transition from the topological Majorana bound state to the trivial Andreev bound state while the ground state energy remains zero. We solve the exact transient transport current and the corresponding differential conductance. The results show that the presence or absence of the interference between the left and right Majorana zero modes plays an important role on the topological phase transition of conductance. It cause the edge-localized topologically trivial states to be insulated with zero conductance, while the nonlocally distributed topologically nontrivial states always have a quantized conductance 2e^2/h. This dramatic change associated with topological phase transition for zero-mode differential conductance at zero bias is independent of the structure of leads and the coupling strength. We also examine the finite size effect of the superconducting chain and the coherence effect between zero mode and non-zero energy modes on the differential conductance in this two-terminal Majorana device.