Floquet-control of Electron Dynamics in Topological Insulator Thin-films

The dynamic control of quantum matter through periodic drives is known as Floquet Engineering, and it is usually achieved by light irradiation. Subjecting a material to monochromatic light has been shown to renormalize its equilibrium bands, leading to the appearance of Floquet (photon-dressed) bands and states. In topological insulators (TIs), the bulk gap guarantees the presence of topologically protected surface states. In the thin film limit, surface states at opposite ends become gapped due to their hybridization. This gap oscillates with the thickness of the thin film, and its opening and closing are accompanied by topological-phase changes. In this work, we consider a TI thin film irradiated with a monochromatic light source. We employ Floquet theory to account for the time periodicity and obtain the quasi-energy spectrum in the resonant regime for various thin-film thicknesses, within the first-order photon resonant approximation. Strikingly, the electron dynamics of the periodically driven TI thin film shows a strong dependence on the film size, and light polarization in the spectrum. We provide a comprehensive analysis of the topological character of the photon-dressed bands by evaluating the Chern numbers for different polarizations, light-matter coupling strengths, and thin-film thicknesses. We demonstrate that it is possible to achieve various topological phase transitions by adjusting these parameters appropriately.