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

Automated summary

This work discusses the energy dependence of the non-Hermitian skin effect (NHSE) by introducing nonreciprocity beyond nearest-neighboring hopping in one-dimensional lattices. It is found that the direction of NHSE reverses as the eigenenergy of the system under open boundary conditions (OBCs) crosses critical energies. The concept of non-Hermitian skin effect edges, which separate the localized eigenstates at opposite ends of the lattice in the OBC spectrum, is introduced to characterize this phenomenon. The skin effect edges are determined by self-intersections in the spectrum under periodic boundary conditions (PBCs) and have topological properties.