Quantized Magnetization Density in Periodically Driven Systems

We study micromotion in two-dimensional periodically driven systems in which all bulk Floquet eigenstates are localized by disorder. We show that this micromotion gives rise to a quantized timeaveraged orbital magnetization density in any region completely filled with fermions. The quantization of magnetization density has a topological origin, and reveals the physical nature of the new phase identified in P. Titum, E. Berg, M. S. Rudner, G. Refael, and N. H. Lindner [Phys. Rev. X 6, 021013 ( 2016)]. We thus establish that the topological index of this phase can be accessed directly in bulk measurements, and propose an experimental protocol to do so using interferometry in cold-atom-based realizations.