Non-Hermitian excitations in nonlinear topological lattice

TL;DR

This paper explores how nonlinearity and non-Hermiticity interact in topological lattice systems, revealing complex behaviors of edge states and effective Hamiltonians in nonlinear photonic and circuit contexts.

Contribution

It demonstrates the interplay between nonlinearity and non-Hermiticity in topological systems using the nonlinear SSH model, highlighting the role of non-Hermitian effective Hamiltonians.

Findings

Non-Hermitian effective Hamiltonian captures the physics of nonlinear topological edge states.

Unconventional time-dependent field localization occurs due to nonreciprocal coupling.

Nonlinear effects influence the stability and properties of topological excitations.

Abstract

Non-linear effects and non-Hermitian phenomena unveil additional intricate facets in topological matter physics. They can naturally intertwine to enable advanced functionalities in topoelectrical circuits and photonic structures. Here, we illustrate the subtle interplay between nonlinearity and non-Hermiticity by examining the characteristics of small wave perturbations on the background of the self-induced topological edge state in the nonlinear Su-Schrieffer-Heeger model. We demonstrate that their underlying physics is captured by the non-Hermitian effective Hamiltonian, which features nonreciprocal coupling terms and entails unconventional time-dependent field localization.