Topological edge solitons and their stability in a nonlinear Su-Schrieffer-Heeger model

TL;DR

This paper investigates topological edge solitons in a nonlinear photonic Su-Schrieffer-Heeger model, demonstrating their existence, stability conditions, and instabilities, with implications for broader 1D nonlinear topological insulators.

Contribution

It establishes the existence and stability criteria of nonlinear edge states in a 1D nonlinear topological insulator with Kerr nonlinearity, extending topological photonics theory.

Findings

Nonlinear edge states exist for all positive energies within the topological band gap.

Edge solitons are stable below a critical coupling ratio.

Instabilities occur at certain energies above the critical ratio.

Abstract

We study continuations of topological edge states in the Su-Schrieffer-Heeger model with on-site cubic (Kerr) nonlinearity, which is a 1D nonlinear photonic topological insulator (TI). Based on the topology of the underlying spatial dynamical system, we establish the existence of nonlinear edge states (edge solitons) for all positive energies in the topological band gap. We discover that these edge solitons are stable at any energy when the ratio between the weak and strong couplings is below a critical value. Above the critical coupling ratio, there are energy intervals where the edge solitons experience an oscillatory instability. Though our paper focuses on a photonic system, we also discuss the broader relevance of our methods and results to 1D nonlinear mechanical TIs.