Adding Doublons to Floquet Topological Insulators

We investigate Floquet topology in a tight-binding model on a finite-sized, two-dimensional, square lattice. Hoppings between neighboring sites vary in time according to a periodic protocol. An appropriate driving protocol makes the bulk of the system insulating while topologically protected edge currents flow around its borders.

A single particle in our two-dimensional system is equivalent to two particles in one dimension. If these two particles interact, they can form doublons, i.e., quasiparticles with both particles localized on the same lattice sites. To model interaction in the two-dimensional system, we modify the lattice sites on the diagonal by adding on-site potentials. This leads to energetically separated, and therefore robust, doublon states which allow the particle to travel along the diagonal.

We combine a driving protocol for the hoppings with a diagonal on-site potential. Small parameter changes flip between particle propagation along the edge and the diagonal.

A possible experimental realization of this Floquet topological system is in a photonic lattice. By flipping between the two propagation modes, light can be steered along the edges or the diagonal of the waveguide array.