  Periodic driving may cause topologically protected, chiral transport along
edges of a 2D lattice that, without driving, would be topologically trivial. We
study what happens if one adds a different on-site potential along the diagonal
of such a 2D grid. In addition to the usual bulk and edge states, the system
then also exhibits doublon states, analogous to two interacting particles in
one dimension. A particle initially located at an edge propagates along the
system's boundary. Its wavefunction splits when it hits the diagonal and
continues propagating simultaneously along the edge and the diagonal. The
strength of the diagonal potential determines the ratio between both parts. We
show that for specific values of the diagonal potential, hopping onto the
diagonal is prohibited so that the system effectively separates into two
triangular lattices. For other values of the diagonal potential, we find a
temporal delay between the two contributions traveling around and through the
system. This behavior could enable the steering of topologically protected
transport of light along the edges and through the bulk of laser-inscribed
photonic waveguide arrays.
