Universal characteristics of one-dimensional non-Hermitian superconductors

Abstract

We establish a non-Bloch band theory for one-dimensional(1D) non-Hermitian topological superconductors. The universal physical properties of non-Hermitian topological superconductors are revealed based on the theory. According to the particle-hole symmetry, there exist reciprocal particle and hole loops of generalized Brillouin zone (GBZ). The critical point of quantum phase transition, where the energy gap closes, appears when the particle and hole loops intersect at Bloch points.If the non-Hermitian system has non-Hermitian skin effects, the non-Hermitian skin effect should be the Z_{2} skin effect: the corresponding eigenstates of particle and hole localize at opposite ends of an open chain, respectively. The non-Bloch band theory is applied to two examples, non-Hermitian p- and s-wave topological superconductors. In terms of Majorana Pfaffian, a Z_{2} non-Bloch topological invariant is defined to establish the non-Hermitian bulk-boundary correspondence in non-Hermitian superconductors.

Generalized bulk-boundary correspondence in periodically driven non-Hermitian systems

“…The non-Hermitian topological superconductors have exhibited many interesting phenomena. The NHSE corresponds to the Z 2 skin effect, and the phase transition occurs at the Bloch points [240]. The interplay between the periodic driving and the particle-hole symmetry may display rich interesting phenomena and this remains to be investigated so far.…”