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

Understanding how local potentials affect system eigenmodes is crucial for experimental studies of nontrivial bulk topology. Recent studies have discovered many exotic and highly nontrivial 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 the Su-Schrieer-Heeger 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.