Non-Hermitian skin effect edge

Non-Hermitian skin effect (NHSE) is a unique phenomenon studied intensively in non-Hermitian systems during the past few years. In this work, we discuss energy dependence of NHSE by introducing nonreciprocity beyond nearest-neighboring hopping one-dimensional lattices. The direction reverses as eigenenergy system under open boundary conditions (OBCs) sweeps across some critical energies. To characterize such phenomenon, introduce concept edges, which separate eigenstates localized at opposite ends lattice OBC spectrum. We find edges are determined self-intersections spectrum periodic (PBCs), topological winding number PBC changes sign when crossing them. Moreover, will disappear merge into single point tuning parameters. Our work reveals intricate interplay between and nonreciprocal systems.