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

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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.