Bello, M.Creffield, Charles E.Platero, G.2023-06-172023-06-172017-03-072469-995010.1103/PhysRevB.95.094303https://hdl.handle.net/20.500.14352/17790©2017 American Physical Society. We would like to thank A. Gómez-León for enlighten- ing discussions. M.B. and G.P. were supported by Spain’s MINECO through Grant No. MAT2014-58241-P, and C.E.C. was supported by Grant No. FIS2013-41716-PWe analyze the dynamics of two strongly interacting fermions moving in two-dimensional 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 allows 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 to a particular sublattice if different sites in the unit cell have different coordination numbers. Contrary to what happens in one-dimensional systems, here we observe the coexistence of both topological and Shockley-like edge states when the system is in a nontrivial phase.engjournal articlehttp://dx.doi.org/10.1103/PhysRevB.95.094303https://journals.aps.orgopen access538.9Optical LatticesTransportNetworksWalksModelFísica de materialesFísica del estado sólido2211 Física del Estado Sólido