Diagnosis of bulk phase diagram of non-reciprocal topological lattices by impurity modes

Abstract

We study the single impurity problem in the non-Hermitian lattice described by the non-reciprocal Su-Schrieffer-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 number of bound states. Particularly, in the limit of strong impurity potential, we find that the phase boundaries of mid-gap bound states are identical to the boundaries of topological phase diagrams of the bulk system in the absence of impurity. The existence of correspondence between mid-gap impurity modes and bulk phases indicate that we are able to diagnose the bulk phase diagram of the non-reciprocal topological model by its impurity modes.

10 pages, 10 figures, version accepted by PRB

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• Non-Hermitian skin effect as an impurity problem
• Nonlinear non-Hermitian skin effect
• The topological counterparts of non-Hermitian SSH models
• Hybrid scale-free skin effect in non-Hermitian systems: A transfer matrix approach
• Fate of Two-Particle Bound States in the Continuum in non-Hermitian Systems
• Point-Gap Bound States in Non-Hermitian Systems
• Topology of multiple cross-linked Su-Schrieffer-Heeger chains
• Berry curvature inside parity-time-symmetry protected exceptional surface
• Quasi-stationary solutions in non-Hermitian systems
• Impurity-induced counter skin-effect and linear modes in non-Hermitian systems
• Exact solutions of non-Hermitian chains with asymmetric long-range hopping under specific boundary conditions
• Bound states and local topological phase diagram of classical impurity spins coupled to a Chern insulator
• Single impurity-induced localization transitions in electronic systems