Quantized magnetization density in periodically driven systems

TL;DR

This paper demonstrates that in disordered, periodically driven 2D systems, the micromotion induces a quantized time-averaged magnetization density and boundary current, linked to a topological winding number, measurable via cold atom experiments.

Contribution

It reveals a topological quantization of magnetization in Floquet systems and connects it to a winding number, enabling bulk measurement through interferometry.

Findings

Quantized time-averaged magnetization density in driven disordered systems.

Boundary currents flow in regions with filled fermions.

Winding number invariant can be measured via bulk interferometry.

Abstract

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 time-averaged magnetization density when the system is filled with fermions. Furthermore we find that a quantized current flows around the boundary of any filled region of finite extent. The quantization has a topological origin: we relate the time-averaged magnetization density to the winding number characterizing the new phase identified in Phys. Rev. X 6, 021013 (2016). We thus establish that the winding number invariant can be accessed directly in bulk measurements, and propose an experimental protocol to do so using interferometry in cold atom based realizations.