Universal characteristics of one-dimensional non-Hermitian superconductors

TL;DR

This paper develops a non-Bloch band theory for 1D non-Hermitian topological superconductors, revealing universal properties, phase transition criteria, and a Z2 topological invariant that extends bulk-boundary correspondence.

Contribution

It introduces a non-Bloch band framework for non-Hermitian superconductors, establishing universal properties, phase transition points, and a topological invariant based on Majorana Pfaffian.

Findings

Critical points occur at |eta|=1 where energy gaps close.

Skin modes are Z2 localized at opposite ends.

Topological phase transitions at eta_{c}= ext{±}1.

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.