Valley Hall edge solitons in a photonic graphene

TL;DR

This paper predicts and analyzes the formation of topologically protected valley Hall edge solitons in a nonlinear photonic graphene with broken inversion symmetry, demonstrating their stability and propagation characteristics.

Contribution

It introduces the concept of valley Hall edge solitons in a nonlinear photonic graphene and explores their properties, including formation, stability, and topological protection.

Findings

Edge solitons bifurcate from linear states at high amplitudes

Modulational instability leads to bright valley Hall edge solitons

Solitons maintain stability through sharp corners of the domain wall

Abstract

We predict the existence and study properties of the valley Hall edge solitons in a composite photonic graphene with a domain wall between two honeycomb lattices with broken inversion symmetry. Inversion symmetry in our system is broken due to detuning introduced into constituent sublattices of the honeycomb structure. We show that nonlinear valley Hall edge states with sufficiently high amplitude bifurcating from the linear valley Hall edge state supported by the domain wall, can split into sets of bright spots due to development of the modulational instability, and that such an instability is a precursor for the formation of topological bright valley Hall edge solitons localized due to nonlinear self-action and travelling along the domain wall over large distances. Topological protection of the valley Hall edge solitons is demonstrated by modeling their passage through sharp corners of the $\Omega$-shaped domain wall.