Relation between PT-symmetry breaking and topologically nontrivial phases in the Su-Schrieffer-Heeger and Kitaev models

Non-Hermitian systems with PT symmetry can possess purely real eigenvalue spectra. In this work two one-dimensional systems with two different topological phases, the topological nontrivial phase (TNP) and the topological trivial phase (TTP), combined with PT-symmetric non-Hermitian potentials are investigated. The models of choice are the Su-Schrieffer-Heeger (SSH) model and the Kitaev chain. The interplay of a spontaneous PT-symmetry breaking due to gain and loss with the topological phase is different for the two models. The SSH model undergoes a PT-symmetry breaking transition in the TNP immediately with the presence of a nonvanishing gain and loss strength γ, whereas the TTP exhibits a parameter regime in which a purely real eigenvalue spectrum exists. For the Kitaev chain the PT-symmetry breaking is independent of the topological phase. We show that the topologically interesting states---the edge states---are the reason for the different behaviors of the two models and that the intrinsic particle-hole symmetry of the edge states in the Kitaev chain is responsible for a conservation of PT symmetry in the TNP.