Topological states in one-dimensional 𝒫𝒯-symmetric non-Hermitian spin-orbit-coupled Su–Schrieffer–Heeger lattices

Abstract

Abstract Energy and topological-state properties of the one-dimensional non-Hermitian spin-orbit-coupled Su–Schrieffer–Heeger lattice are theoretically investigated by introducing spin-dependent onsite imaginary potentials with gain and loss. It is found that imaginary potentials lead to the appearance of imaginary energies in the topologically nontrivial phase region, and ${\cal {PT}}$ phase transition occurs in the topologically trivial region. In addition, the imaginary potentials and spin–orbit coupling act together to make the topological phase transition occur in the topologically trivial region, and the topologically nontrivial region becomes wider. The energy spectrum results show that imaginary potentials and spin–orbit coupling have obvious effects on the zero-energy edge states of this system, which mainly lie in the presence of four types of zero-energy states with different localization and numbers. Furthermore, we discuss diagonal disorder and the transport behavior of system, further characterizing the properties of the individual topological states. The above results indicate the special adjustment effect of imaginary potentials and spin–orbit coupling on the band structure of such a system.