Floquet superlattices and edge states in graphene nanoribbons

Structured light provides a route to imprint spatially patterned Floquet potentials onto quantum materials. As a particular example, we study a zigzag graphene nanoribbon driven by two coherent tilted beams, whose interference creates a periodic polarization pattern that gives rise to a photo-induced superlattice. The matching between the periodicity of the optical field and the nanoribbon width leads to two regimes in the quasienergy spectrum: matched profiles preserve degenerate edge branches, while mismatched profiles yield a boundary-induced gap that survives in wide ribbons. We propose a two-edge model that captures this splitting through residual hybridization and the boundary-sampled optical field. The quasienergy gap reverses between valleys, leading to a valley-selective boundary response. Our results establish light-induced superlattices as a flexible method for valley selectivity in finite-size Dirac-like materials through tunable edge-state quasienergy splitting.