# Non-Hermitian Majorana modes protect degenerate steady states

## TL;DR

This paper explores non-Hermitian generalizations of Majorana zero modes in a dissipative Kitaev chain, revealing their role in protecting degenerate steady states and extending topological classifications to non-Hermitian systems.

## Contribution

It introduces non-Hermitian Majorana modes in dissipative systems, analyzes their stability, and maps the problem to known models, expanding topological phase understanding.

## Key findings

- MZMs ensure two-fold degeneracy in steady states
- Effective Hamiltonian retains BDI classification with non-Hermitian modifications
- Topological phase diagram and stability conditions are established

## Abstract

We introduce non-Hermitian generalizations of Majorana zero modes (MZMs) which appear in the topological phase of a weakly dissipative Kitaev chain coupled to a Markovian bath. Notably, the presence of MZMs ensures that the steady state in the absence of decoherence events is two-fold degenerate. Within a stochastic wavefunction approach, the effective Hamiltonian governing the coherent, non-unitary dynamics retains BDI classification of the closed limit, but belongs to one of four non-Hermitian "flavors" of the ten-fold way. We argue for the stability of MZMs due to a generalization of particle-hole symmetry, and uncover the resulting topological phase diagram. Qualitative features of our study generalize to two-dimensional chiral superconductors. The dissipative superconducting chain can be mapped to an Ising model in a complex transverse field, and we discuss potential signatures of the degeneracy.