# Topological quantum wires with balanced gain and loss

## TL;DR

This paper investigates a topological superconductor model with balanced gain and loss, revealing how non-Hermitian effects influence topological phases, edge states, and phase stability through analytical and numerical analysis.

## Contribution

It introduces a framework for analyzing topological superconductors with non-Hermitian, $ ext{PT}$-symmetric potentials, deriving a bulk invariant and phase diagram.

## Key findings

- Topological phase stability depends on gain/loss strength.
- Edge states remain exponentially localized despite gain and loss.
- The bulk topological invariant is explicitly derived for the non-Hermitian system.

## Abstract

We study a one-dimensional topological superconductor, the Kitaev chain, under the influence of a non-Hermitian but $\mathcal{PT}$-symmetric potential. This potential introduces gain and loss in the system in equal parts. We show that the stability of the topological phase is influenced by the gain/loss strength and explicitly derive the bulk topological invariant in a bipartite lattice as well as compute the corresponding phase diagram using analytical and numerical methods. Furthermore we find that the edge state is exponentially localized near the ends of the wire despite the presence of gain and loss of probability amplitude in that region.