Topological properties in an Aubry–André–Harper model with p-wave superconducting pairing

Abstract

Abstract We study the topological properties of the one-dimensional p-wave Aubry–André–Harper (AAH) model with periodic incommensurate potential and transition coupling. The calculation results show that due to co-influence of the incommensurate potential and modulation phase, three topological phases arise in different parameter regions: a topologically trivial phase, Su–Schrieffer–Heeger (SSH)-like topological phase, and Kitaev-like topological superconducting phase with Majorana zero modes. By evaluating the Andreev reflection conductance, we see that in the Kitaev-like phase, the quantized conductance plateau comes into being at the zero-bias limit, due to the occurrence of resonant Andreev reflection. In addition, when the disorder effect is incorporated, the SSH-like topology is modified sensitively and the degenerate topological states split, whereas the Kitaev-like topological phase is robust to weak disorder. Finally, we find that disorder can induce topological phase transition, i.e. from the topologically trivial phase to the topological phase. Based on these results, we believe that our findings have significance for studying the topological phase transition in a one-dimensional topological superconducting system. Also, it provides a feasible scheme for clarifying different topological phases.