Coupling of Edge States and Topological Bragg Solitons.

The existence of the edge states at the interface between two media with different topological properties is protected by symmetry, which makes such states robust against structural defects or disorder. We show that, if a system supports more than one topological edge state at the interface, even a weak periodic deformation may scatter one edge state into another without coupling to bulk modes. This is the Bragg scattering of the edge modes, which in a topological system is highly selective, with closed bulk and backward scattering channels, even when conditions for resonant scattering are not satisfied. When such a system bears nonlinearity, Bragg scattering enables the formation of a new type of soliton-topological Bragg solitons. We report them in a spin-orbit-coupled (SOC) Bose-Einstein condensate in a homogeneous honeycomb Zeeman lattice. An interface supporting two edge states is created by two different SOCs, with the y component of the synthetic magnetic field having opposite directions at different sides of the interface. The reported Bragg solitons are found to be stable.