Floquet X-Ray Scattering as a Probe of Hidden Electronic Orders

We develop a theoretical framework for Floquet resonant X-ray scattering, using Floquet theory combined with the ultrashort core-hole lifetime expansion. We obtain a compact expression for the Floquet components of the resonant inelastic X-ray scattering operator, which shows that Floquet X-ray scattering provides direct access to bond and current correlations that do not directly produce charge Bragg peaks in conventional diffraction. Applying this framework to charge-ordered states on the Kagome lattice, we demonstrate that different symmetry-breaking orders exhibit distinct polarization fingerprints in the Floquet Bragg peaks. Moreover, the relative weight of bond and current contributions can be tuned through the drive frequency. These results establish Floquet X-ray scattering as a symmetry-resolved probe of hidden electronic order or fluctuations in quantum materials.