# Bulk soliton dynamics in bosonic topological insulators

## TL;DR

This paper investigates the behavior of vortex solitons in nonlinear bosonic topological insulators, revealing their stability, dynamics influenced by Berry curvature, and their ability to generate chiral edge states upon boundary interaction.

## Contribution

It introduces a new continuum Dirac model to describe vortex solitons and demonstrates their unique topological interactions and stability in a nonlinear topological lattice.

## Key findings

- Stable vortex solitons exist within the topological band gap.
- Soliton dynamics are affected by Berry curvature and anomalous velocity.
- Boundary interactions produce chiral edge states and anomalous reflections.

## Abstract

We theoretically explore the dynamics of spatial solitons in nonlinear/interacting bosonic topological insulators. We employ a time-reversal broken Lieb-lattice analog of a Chern insulator and find that in the presence of a saturable nonlinearity, solitons bifurcate from a band of non-zero Chern number into the topological band gap with vortex-like structure on a sublattice. We numerically demonstrate the existence stable vortex solitons for a range of parameters and that the lattice soliton dynamics are subject to the anomalous velocity associated with large Berry curvature at the topological Lieb band edge. The features of the vortex solitons are well described by a new underlying continuum Dirac model. We further show a new kind of interaction: when these topological solitons `bounce' off the edge of a finite structure, they create chiral edge states, and this give rise to an "anomalous" reflection of the soliton from the boundary.