Attosecond electron dynamics in Floquet phases probed with time-resolved ARPES from TDDFT

Light-driven Floquet band engineering has recently emerged as a promising technique for controlling material properties. Floquet phases are typically probed with time- and angle-resolved photoelectron spectroscopy (Tr-ARPES), providing direct access to the driven electronic bands. Applications of Tr-ARPES to date focused on observing the Floquet bands themselves, their build-up, and their dephasing, but have not explored sub-laser-cycle dynamics within those bands. Given that Floquet theory is applicable only in time-periodic conditions, the notion of resolving sub-laser-cycle dynamics between Floquet states seems contradictory – it requires probe pulse durations shorter than a single laser cycle, which inherently cannot discern the time-periodic nature of the light-matter system. We propose to employ attosecond pulse train probes with the same temporal periodicity as the Floquet-dressing pump pulse, allowing both attosecond sub-laser-cycle resolution, and a projection of Tr-ARPES spectra on the Floquet bands. We employ this approach in ab-initio calculations of light-driven graphene. Our calculations predict significant sub-laser-cycle dynamics occurring within the Floquet phase with the majority of electrons moving in-between Floquet bands, and a small portion residing and moving outside of them in what we denote as ‘non-Floquet’ bands. This work indicates that the Floquet-Bloch states are not a complete basis set for sub-laser-cycle dynamics in steady-state phases of matter.