Floquet-topological behavior of finite and infinite square lattices with different driving schemes

We investigate a tight-binding model of a single particle on a two-dimensional, square lattice with periodic boundary conditions (PBC) in both spatial dimensions (bulk), PBC in only one dimension (strip geometry), as well as finite systems.

Hoppings between neighboring sites vary according to discrete, temporally and spatially periodic driving schemes. Some schemes allow topologically protected edge currents to flow around the system's borders while its bulk remains insulating. Such systems are called Floquet-topological insulators.

In addition to hoppings, the system's Hamiltonian contains on-site potentials, varying for individual or groups of lattice sites. Possible variations are single-site defects, linear disruptions, or spatially periodic (e.g., alternating) variations.

By varying the hopping scheme and on-site potentials, we can confine the particle to a localized, periodic movement (insulating behavior) or switch to long-range motion through the system (conducting). In an experimental realization in photonic lattices, this corresponds to steering light within a waveguide array.