Quantized transport in periodically driven quantum systems

Periodically driven quantum systems, such as semiconductors subject to light and cold atoms in optical lattices, provide a novel and versatile platform for realizing topological phenomena. Among these are analogs of topological insulators and superconductors, attainable in static systems. However, some of these phenomena are unique to the periodically driven case.  I will describe how the interplay between periodic driving, disorder, and interactions gives rise to new steady states exhibiting robust topological phenomena, with no analogues in static systems. Specifically, I will show that disordered two dimensional driven systems admit an “anomalous" phase with chiral edge states that coexist with a fully localized bulk. This phase serves as a basis for new far-from-equilibrium quantized transport phenomena. Specifically, I will discuss the quantization of magnetization and two terminal currents in this anomalous phase.