Self-induced topological transitions and edge states supported by nonlinear staggered potentials

TL;DR

This paper explores how Kerr nonlinearities in SSH arrays induce self-driven topological phase transitions and edge states, revealing new localized solutions and dynamic behaviors dependent on intensity.

Contribution

It introduces a novel class of nonlinear topological edge states in SSH arrays caused by Kerr effects, expanding understanding of topological insulators in nonlinear regimes.

Findings

Nonlinear SSH arrays support self-induced topological transitions.

Localized edge states decay to a non-zero amplitude plateau.

Conditions for nonlinear topological states are derived.

Abstract

The canonical Su-Schrieffer-Heeger (SSH) model is one of the basic geometries that have spurred significant interest in topologically nontrivial bandgap modes with robust properties. Here, we show that the inclusion of suitable third-order Kerr nonlinearities in SSH arrays opens rich new physics in topological insulators, including the possibility of supporting self-induced topological transitions based on the applied intensity. We highlight the emergence of a new class of topological solutions in nonlinear SSH arrays, localized at the array edges. As opposed to their linear counterparts, these nonlinear states decay to a plateau with non-zero amplitude inside the array, highlighting the local nature of topologically nontrivial bandgaps in nonlinear systems. We derive the conditions under which these unusual responses can be achieved, and their dynamics as a function of applied intensity. Our work paves the way to new directions in the physics of topologically non-trivial edge states with robust propagation properties based on nonlinear interactions in suitably designed periodic arrays.