Diagnosis of bulk phase diagram of nonreciprocal topological lattices by impurity modes

We study the single-impurity problem in the non-Hermitian lattice described by the nonreciprocal SuSchrieffer-Heeger model and obtain the phase diagram of localized bound states induced by the impurity. The existence of analytical results permits us to determine the phase boundaries exactly, which separate regions with different numbers of bound states. Particularly, in the limit of the strong impurity potential, we find that the phase boundaries of midgap bound states are identical to the boundaries of topological phase diagrams of the bulk system in the absence of impurities. The existence of a correspondence between midgap impurity modes and bulk phases indicates that we are able to diagnose the bulk phase diagram of the nonreciprocal topological model by its impurity modes.