Observing Floquet-Bloch States in van der Waals Semiconductors

Floquet engineering has generated much interest in recent years as a powerful approach to manipulating the electronic structure and topology in the material and manifest quantum states otherwise inaccessible in equilibrium. Typically, an intense optical field is used to create the Floquet states in materials1–3. Despite its potential, the experimental realizations of Floquet engineering using optical fields have been challenging due to detrimental effects such as multi-photon absorption, heating, and scattering. Recently, oscillating bosonic fields within the material, such as excitons or phonons, have been proposed as an alternate route to Floquet engineering4. In the case of the exciton, its presence in the material alters the original ground state Hamiltonian by dynamically changing the many-electron screened-exchange interaction. This results in a time-dependent coupling that oscillates periodically at the exciton frequency and is responsible for driving the Floquet states in the material. So far, such proposals of Floquet engineering driven by quasi-particle fields, such as excitons, have not been achieved experimentally.<br/>In this work, using time-resolved angle-resolved photoemission spectroscopy (tr-ARPES), we show that the valence band in monolayer tungsten disulfide (WS2) gets replicated in energy due to the oscillating field generated by excitons. We find that the strength of the exciton-driven Floquet effect is two orders of magnitude stronger than the optically driven counterpart. Consequently, we observe that the exciton-driven Floquet replica of the conduction band hybridizes with the bare valence band resulting in a distinct Mexican-hat-like dispersion with a local dip at the center of the valence band. This work also reproduces the predicted changes in the band structure for the BEC to BCS transition in non-equilibrium excitonic insulators. Our findings open new avenues to Floquet engineering using quasi-particle fields such as excitons, phonons, or plasmons.<br/>References<br/>1. Wang, Y. H., Steinberg, H., Jarillo-Herrero, P. & Gedik, N. Observation of Floquet-Bloch states on the surface of a topological insulator. Science 342, 453–457 (2013).<br/>2. Mahmood, F. et al. Selective scattering between Floquet–Bloch and Volkov states in a topological insulator. Nat. Phys. 12, 306–310 (2016).<br/>3. Aeschlimann, S. et al. Survival of Floquet–Bloch States in the Presence of Scattering. Nano Lett. 21, 5028–5035 (2021).<br/>4. De Giovannini, U. & Hübener, H. Floquet analysis of excitations in materials. J. Phys. Mater. 3, 012001 (2019).<br/><br/>Vivek Pareek, David Bacon and Xing Zhu contributed equally to this work.<br/>Corresponding authors: Felipe H. da Jornada and Keshav Dani.