Light-driven Superlattices in Dirac-like Systems*

Optical driving offers fine control of matter, yet conventional approaches, such as tuning intensity, frequency, and polarization, use only part of light’s capability. Spatially structured beams add a powerful knob, imprinting spatiotemporal order. We study graphene irradiated by a monochromatic beam with a one-dimensional (1D), periodically modulated intensity. Moreover, we drive our material with circularly polarized light, which in contrast to standard linear polarization will result in an effective mass. Utilizing Floquet theory, we construct the space–time–dependent Floquet Hamiltonian and, in the high-frequency limit, derive a stroboscopic effective description with 1D spatial periodicity. We solve analytic transcendental equations to obtain the photo-dressed quasi-energy spectrum and provide a complete characterization of the emergent light-induced states. Our description reveals how spatially structured periodic drives shape the spectrum and electronic states.