Anomalous edge states and the bulk-edge correspondence for periodically-driven two dimensional systems

Recently, several authors have investigated topological phenomena in-driven systems of non-interacting particles. These phenomena are through analogies between the Floquet spectra of driven systems and band structures of static Hamiltonians. Intriguingly, these works have that the topological characterization of driven systems is richer than of static systems. In particular, in driven systems in two dimensions(2D), robust chiral edge states can appear even though the Chern numbers of all bulk Floquet bands are zero. Here we elucidate the crucial distinctions static and driven 2D systems, and construct a new topological invariant yields the correct edge state structure in the driven case. We provide in both the time and frequency domains, which afford additional into the origins of the "anomalous" spectra which arise in driven. Possible realizations of these phenomena in solid state and cold systems are discussed.