Quantized Chern-Simons Axion Coupling in Anomalous Floquet Systems

Abstract: 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, 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, cross-correlated responses such as 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.