Majorana Edge Modes with Gain and Loss

TL;DR

This paper investigates the existence of stable Majorana zero modes in a non-Hermitian Kitaev model with gain and loss, revealing conditions under which these modes persist despite non-Hermiticity and disorder.

Contribution

It introduces a non-Hermitian extension of the Kitaev model demonstrating the stability of Majorana modes under gain, loss, and disorder, with specific symmetry conditions.

Findings

Majorana zero modes exist at zero chemical potential with random gain and loss.

Majorana modes can appear at non-zero chemical potential if the non-Hermitian part is PT symmetric.

Stable Majorana modes are possible in non-Hermitian systems with specific symmetry constraints.

Abstract

We consider a non-Hermitian generalization of the Kitaev model and study the existence of stable Majorana zero energy modes. We show that they exist in the limit of zero chemical potential even if balanced gain and loss are randomly distributed along the lattice. We show that Majorana zero modes also appear if the chemical potential is different from zero provided that not the full Hamiltonian but the non-Hermitian part of the Hamiltonian is PT symmetric.