Light-modulation- and Ribbon-length Commensurability Effects in Floquet-driven Graphene

Floquet engineering provides a robust framework for exploring novel phases of quantum matter, thus enabling dynamic control over material properties through periodic driving. Traditionally, Floquet control of materials has been accomplished through homogeneous light irradiation by tuning the light's intensity, frequency, and polarization. In this work, we subject a zigzag-terminated graphene nanoribbon to two monochromatic beams with different angles of incidence and tuning parameters. The interference between these two beams results in a system with a periodic spatiotemporal profile due to the variation of intensity and polarization across the nanoribbon. In the high-frequency limit, the effect of light mimics a periodic Jackiw-Rebi model in the bulk of the nanoribbon. The main spectral features of the driven system can be captured via an effective model for the edge states. Strikingly, this model demonstrates that the critical parameter dominating the spectrum is the commensurability between the polarization profile and the ribbon width, in good agreement with the numerically calculated bulk spectrum.