# Symmetry-protected localized states at defects in non-Hermitian systems

## TL;DR

This paper explores how local potentials in non-Hermitian systems can induce symmetry-protected localized states, including zero-energy modes and bound states, which are robust against symmetry-preserving perturbations.

## Contribution

It generalizes the concept of symmetry-protected localized states to non-Hermitian systems, analyzing their emergence and robustness near defects.

## Key findings

- Vacancies induce zero-energy modes protected by chiral symmetry.
- Localized bound states with purely imaginary eigenvalues appear near defects.
- These states are robust against symmetry-preserving perturbations.

## Abstract

Understanding how local potentials affect system eigenmodes is crucial for experimental studies of nontrivial bulk topology. Recent studies have discovered many exotic and highly non-trivial topological states in non-Hermitian systems. As such, it would be interesting to see how non-Hermitian systems respond to local perturbations. In this work, we consider chiral and particle-hole -symmetric non-Hermitian systems on a bipartite lattice, including SSH model and photonic graphene, and find that a disordered local potential could induce bound states evolving from the bulk. When the local potential on a single site becomes infinite, which renders a lattice vacancy, chiral-symmetry-protected zero-energy mode and particle-hole symmetry-protected bound states with purely imaginary eigenvalues emerge near the vacancy. These modes are robust against any symmetry-preserved perturbations. Our work generalizes the symmetry-protected localized states to non-Hermitian systems.