Nonlinear edge modes from topological 1D lattices

TL;DR

This paper introduces a method to study topological edge modes in 1D nonlinear lattices by deforming linear modes into nonlinear solutions, revealing conditions for their protection and disappearance.

Contribution

It presents a novel approach to analyze nonlinear topological edge modes by deforming linear solutions and identifies symmetry conditions that protect these modes.

Findings

Nonlinear edge modes can be deformed from linear modes.

Certain nonlinearities with generalized chiral symmetry protect edge modes.

Edge modes may disappear at high nonlinearities when shifted out of the energy gap.

Abstract

We propose a method to address the existence of topological edge modes in one-dimensional (1D) nonlinearlattices, by deforming the edge modes of linearized models into solutions of the fully nonlinear system. Forlarge enough nonlinearites, the energy of the modified edge modes may eventually shift out of the gap, leadingto their disappearance. We identify a class of nonlinearities satisfying a generalised chiral symmetry wherethis mechanism is forbidden, and the nonlinear edge states are protected by a topological order parameter.Different behaviours of the edge modes are then found and explained by the interplay between the nature of thenonlinarities and the topology of the linearized models.