  Recently, several authors have investigated topological phenomena in
periodically-driven systems of non-interacting particles. These phenomena are
identified through analogies between the Floquet spectra of driven systems and
the band structures of static Hamiltonians. Intriguingly, these works have
revealed that the topological characterization of driven systems is richer than
that 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
the bulk Floquet bands are zero. Here we elucidate the crucial distinctions
between static and driven 2D systems, and construct a new topological invariant
that yields the correct edge state structure in the driven case. We provide
formulations in both the time and frequency domains, which afford additional
insight into the origins of the "anomalous" spectra which arise in driven
systems. Possible realizations of these phenomena in solid state and cold
atomic systems are discussed.
