Bulk soliton dynamics in bosonic topological insulators

We theoretically explore the dynamics of spatial solitons in nonlinear or 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, stable solitons bifurcate from a band of nonzero Chern number into the topological band gap with vortexlike structure on a sublattice. We numerically demonstrate the existence stable vortex solitons for a range of parameters and that the lattice soliton dynamics is 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 an underlying continuum Dirac model. We further show a different 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.