A class of stable nonlinear non-Hermitian skin modes

TL;DR

This paper investigates the existence and stability of nonlinear non-Hermitian skin modes in one-dimensional lattices, revealing conditions for their presence and how nonreciprocity influences their survival in finite systems.

Contribution

It introduces a method to achieve stable localized nonlinear skin modes and analyzes their survival time depending on system parameters and nonreciprocity.

Findings

Quasi-skin modes can exist in nonlinear nonreciprocal lattices.

Survival time of skin modes depends on system parameters.

Nonreciprocity affects the stability and localization of skin modes.

Abstract

The non-Hermitian skin effect (NHSE) is a well-known phenomenon in open topological systems that causes a large number of eigenstates to become localized at the boundary. Although many aspects of its theory have been investigated in linear systems, this phenomenon remains novel in nonlinear models. In the first step of this paper, we look at the conditions for the presence of quasi-skin modes in a semi-infinite, one-dimensional, nonlinear, nonreciprocal lattice. In the following phase, we explore the survival time of the quasi-skin mode in a finite nonlinear lattice with open edges. We study the dependency of the survival time on the system's parameters and demonstrate how the nonreciprocity of the system affects the survival time. This study introduces a method for achieving a stable localized state in a nonlinear finite lattice.