Band structure of the one-dimensional tetrameric Kitaev chain induced by imaginary potentials

We investigate the one-dimensional tetramerised Kitaev chain induced by imaginary potentials $\{i\gamma ,-i\gamma ,-i\gamma ,i\gamma \}$ applied to the dimerised Kitaev chain. It is found that the imaginary potentials cause a variety of topological phase transitions. When the chemical potential $\mu$ is tuned to the energy zero point, they lead to the appearance of the mixed phase of the system consisting of two purely real Kitaev-like modes and four purely imaginary energy SSH-like zero-energy modes, which appear as the transition of the Kitaev-like-mixed-SSH-like phase. In addition, the Kitaev-like phase can be broadened by imaginary potentials, manifested as the widening of the quantised Andreev reflection plateau. When $\mu \ne 0$, the same topological phase transition occurs, from the topologically-trivial phase to the Kitaev-like phase. One can believe that this work provides theoretical support for probing the generation of Majorana zero modes in new topological superconducting systems.