Nonlinear non-Hermitian skin effect

TL;DR

This paper investigates the nonlinear non-Hermitian skin effect, revealing how edges influence localized solutions and band structures in nonlinear lattices, with implications for designing novel nonlinear materials.

Contribution

It introduces the study of nonlinear non-Hermitian skin effect, showing edge effects on stationary solutions and band structures in nonlinear lattices, including fractal and continuum bands.

Findings

Stationary solutions localize at edges in continuum bands

Fractal and continuum bands emerge in nonlinear lattices

Nonlinear exceptional points vanish in infinite lattices

Abstract

Distant boundaries in linear non-Hermitian lattices can dramatically change energy eigenvalues and corresponding eigenstates in a nonlocal way. This effect is known as non-Hermitian skin effect (NHSE). Combining non-Hermitian skin effect with nonlinear effects can give rise to a host of novel phenomenas, which may be used for nonlinear structure designs. Here we study nonlinear non-Hermitian skin effect and explore nonlocal and substantial effects of edges on stationary nonlinear solutions. We show that fractal and continuum bands arise in a long lattice governed by a nonreciprocal discrete nonlinear Schrodinger equation. We show that stationary solutions are localized at the edge in the continuum band. We consider a non-Hermitian Ablowitz-Ladik model and show that nonlinear exceptional point disappears if the lattice is infinitely long.