Topological phase in a nonreciprocal Kitaev chain

Abstract

We systematically investigate the nonreciprocal Kitaev chain, where the nonreciprocity arises from the hopping amplitude and pairing strength. By studying the Hamiltonians under three different bases, we reveal that the nonreciprocal hopping amplitude cannot induce a topological phase transition, but can result in the complex energy spectrum and non-Hermitian skin effect. Moreover, the Majorana zero energy edge modes, which are robust against the nonreciprocal hopping amplitude, exist stably in the topologically nontrivial phase. On the other hand, the nonreciprocal pairing strength can trigger a topological phase transition, which is associated with the pseudo-Hermitian symmetry breaking. More interestingly, we observe that the exceptional points independent of the topological phase can be determined by the dispersion relation, and there is no non-Hermitian skin effect in the system. Furthermore, we calculate the topological invariant to demonstrate the validity of the bulk-edge correspondence in the pseudo-Hermitian symmetry-unbroken region. Our investigation provides a path to explore the fundamental physics pertaining to the interplay between nonreciprocity and topology in the non-Hermitian topological superconductors.