Quantized Chern-Simons Axion Coupling in Anomalous Floquet Systems

TL;DR

This paper demonstrates that two-dimensional anomalous Floquet systems can exhibit a quantized bulk response characterized by a Chern-Simons axion coupling, revealing a topological magnetoelectric effect in driven systems.

Contribution

It introduces a framework to understand quantized bulk responses in Floquet systems via a Chern-Simons axion coupling angle, connecting Floquet band topology to observable effects.

Findings

Quantized CSA coupling angle in Floquet systems

Emergence of photon dimension as a third dimension

Physical signatures like photon-space polarization

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.