Anomalous Edge States and the Bulk-Edge Correspondence for Periodically Driven Two-Dimensional Systems

Recently, several authors have investigated topological phenomena in periodically driven systems of noninteracting 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 phenomena that cannot be characterized by analogy to the topological classification framework for 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 that arise in driven systems. Possibilities for realizing these phenomena in solid-state and cold-atomic systems are discussed.