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 and their values of GBZ satisfy |\beta| = 1. If the non-Hermitian system has skin modes, these modes should be Z2 style, i.e., 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. Topological phase transitions occur at \beta_{c}= \pm 1 in the two systems. In terms of Majorana Pfaffian, a Z2 non-Bloch topological invariant is defined to establish the non-Hermitian bulk-boundary correspondence in non-Hermitian superconductors.