Exploring nonlinear topological states of matter with exciton-polaritons: Edge solitons in kagome lattice

TL;DR

This paper demonstrates the existence of nonlinear topological edge solitons in exciton-polariton fluids within a kagome lattice, revealing new stable localized excitations with controllable velocities due to the lattice's unique topological properties.

Contribution

It introduces the concept of topological edge solitons in exciton-polariton systems and shows their properties through theoretical and numerical analysis, highlighting their stability and controllability.

Findings

Existence of bright, dark, and grey topological edge solitons.

Solitons can be described by nonlinear Schrödinger equation in certain regimes.

Collision of solitons is elastic, confirming their solitonic nature.

Abstract

Matter in nontrivial topological phase possesses unique properties, such as support of unidirectional edge modes on its interface. It is the existence of such modes which is responsible for the wonderful properties of a topological insulator -- material which is insulating in the bulk but conducting on its surface, along with many of its recently proposed photonic and polaritonic analogues. We show that exciton-polariton fluid in a nontrivial topological phase in kagome lattice, supports nonlinear excitations in the form of solitons built up from wavepackets of topological edge modes -- topological edge solitons. Our theoretical and numerical results indicate the appearance of bright, dark and grey solitons dwelling in the vicinity of the boundary of a lattice strip. In a parabolic region of the dispersion the solitons can be described by envelope functions satisfying the nonlinear Schr\"odinger equation. Upon collision, multiple topological edge solitons emerge undistorted, which proves them to be true solitons as opposed to solitary waves for which such requirement is waived. Importantly, kagome lattice supports topological edge mode with zero group velocity unlike other types of truncated lattices. This gives a finer control over soliton velocity which can take both positive and negative values depending on the choice of forming it topological edge modes.