Quantized Chern-Simons Axion Coupling in Anomalous Floquet Systems.

Quantized bulk response functions are hallmark signatures of topological phases, but their manifestation in periodically driven (Floquet) systems is not yet fully established. Here, we show that two-dimensional anomalous Floquet systems exhibit a quantized bulk response encoded in a Chern-Simons axion (CSA) coupling angle θ_{CS}^{F}∈2πZ, reflecting a topological magnetoelectric effect analogous to that in three-dimensional insulators. The periodic drive introduces an emergent "photon" dimension, allowing the system to be viewed as a three-dimensional Sambe lattice. Within this framework, quantized cross-correlated responses-namely, photon-space polarization and magnetization density-emerge as physical signatures of the CSA coupling. The CSA angle, constructed from the non-Abelian Berry connection of Floquet states, admits a natural interpretation in terms of the geometry of hybrid Wannier states. These results provide a unified framework linking Floquet band topology to quantized bulk observables, demystifying the topology of gapped 2D anomalous Floquet systems by establishing their connection to static 3D topological systems.