Anomalous Behavior Induced by a Single Impurity in Non-Hermitian Topological Systems with Nonreciprocal Coupling

A remarkable feature of non-Hermitian topological systems with skin effects is that their spectra and eigenstates are strongly dependent on the choice of boundary conditions. Here, we investigate a system where the impurity couples to a nonreciprocal Su-Schrieffer-Heeger (SSH) chain at two points with nonreciprocal coupling. We first study the spectrum of the system and demonstrate that nonreciprocal couplings between the impurity and the chain alter its spectral structure. Particularly, this effect becomes particularly prominent in the limit of unidirectional coupling, inducing a shift in the parameter regime for the zero mode. Meanwhile, the impurity-chain couplings give rise to two effective boundary conditions and determine the spatial distribution of the zero mode. In addition, the localization of bulk states is significantly altered by tuning the nonreciprocity of the impurity-chain coupling. Notably, in the unidirectional coupling regime, two distinct types of bulk states coexist near the same boundary, one differing from the other in both spatial distribution and degree of localization. We also find that the bulk states undergo significant skin phase transitions as the coupling strength varies, characterized by a transition from conventional skin states to bipolar skin states. Our findings establish the feasibility of controlling non-Hermitian topological systems by coupling an impurity.