Sublattice dynamics and quantum state transfer of doublons in two-dimensional lattices

We study the dynamics of two strongly-interacting fermions moving in 2D lattices under the action of a periodic electric field, both with and without a magnetic flux. Due to the interaction, these particles bind together forming a doublon. We derive an effective Hamiltonian that permits us to understand the interplay between the interaction and the driving, revealing surprising effects that constrain the movement of the doublons. We show that it is possible to confine doublons to just the edges of the lattice, and also to a particular sublattice, if different sites in the unit cell have different coordination numbers. Contrary to what happens in 1D systems, here we observe the coexistence of both topological and Shockley-like edge states when the system is in a non-trivial phase.