Bulk soliton dynamics in bosonic topological insulators

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.

5 pages, 4 figure, comments welcome!!

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• Nonlinear topological photonics
• Topological Frequency Combs and Nested Temporal Solitons
• Stability of topological edge states under strong nonlinear effects
• Probing band topology using modulational instability
• Topological edge solitons and their stability in a nonlinear Su-Schrieffer-Heeger model
• Non-Hermitian topological end breathers
• Tutorial: Classifying Photonic Topology Using the Spectral Localizer and Numerical $K$-Theory
• Topological bulk solitons in a nonlinear photonic Chern insulator
• Self-localized topological states in three dimensions
• A local test for global extrema in the dispersion relation of a periodic graph
• Standing Wave Solutions in Twisted Multicore Fibers