Photo-induced One-dimensional Superlattices in Dirac-like Systems

Optical control of quantum matter has opened new possibilities for precise control of its properties. Traditional optical methods use light intensity, frequency, and polarization as parameters to modify materials, but only partially tap into light's full potential. Light beams with spatial dependent intensity, for example, provide control on emergent spatiotemporal patterns. This work explores the consequences of irradiating graphene with a monochromatic one-dimensional (1D)-periodic modulated light intensity. Using the Floquet theorem, we derive the space-time dependent Floquet Hamiltonian, and within the high-frequency regime, we obtain an effective stroboscopic 1D-space-periodic description. We analytically derive the set of transcendental equations that govern the photo-dressed electronic spectrum for these spatially periodic beams. We present a complete description of the photo-induced states that emerge and analyze the combined effects of spatial- and time-frequencies on the quasienergy spectrum.