  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.
