Non-Hermitian skin effect edge

TL;DR

This paper explores the energy-dependent non-Hermitian skin effect in one-dimensional lattices with extended nonreciprocity, introducing the concept of skin effect edges that separate localized eigenstates and are linked to spectral self-intersections.

Contribution

It introduces the novel concept of non-Hermitian skin effect edges and links their topological nature to spectral self-intersections in nonreciprocal lattice systems.

Findings

Skin effect edges are determined by spectral self-intersections.

The topological nature of skin effect edges is characterized by the winding number.

Skin effect edges disappear when self-intersections merge into a single point.

Abstract

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.