Spontaneous PT-symmetry breaking in non-Hermitian Kitaev and extended Kitaev models

The spontaneous parity-time (PT) symmetry breaking is discussed in non-Hermitian PT-symmetric Kitaev and extended Kitaev models whose Hermiticity is broken by the presence of two conjugated imaginary potentials +/- i gamma at two end sites. In the case of the non-Hermitian Kitaev model, a spontaneous PT-symmetry breaking transition (SPT BT) occurs at a certain gamma(c) in the topologically trivial phase (TTP) region, similar to that of the Su-Schrieffer-Heeger (SSH) model. However, unlike the SSH model, the system also undergoes such a transition in the topologically nontrivial phase (TNP) region. We study an extended Kitaev model by combining the superconducting pairing in the Kitaev model and the staggered hopping in the SSH model. This model contains three different topological phases: the TTP, the Kitaev-like TNP, and the SSH-like TNP. For the non-Hermitian extended Kitaev model, a SPT BT occurs in the Kitaev-like TNP region, as well as in part of the TTP and SSH-like TNP regions, whereas the PT symmetry is broken for an arbitrary nonzero gamma in the rest of the TTP and SSH-like TNP regions. Therefore, we can conclude that there is no universal correlation between topological properties and the SPT BT.