Edge States in Graphene Induced by High-Frequency Irradiation*

Dirac materials, such as graphene, host electrons with linear energy–momentum dispersion and exhibit tunable spectra under external fields, making them an active platform for engineered band structures. In this work, we studied the continuum Hamiltonian model for graphene under a space-periodic polarized light vector potential, with time dependence treated through Floquet theory. Using Van Vleck’s high-frequency approximation, we derived an effective Hamiltonian and applied a finite-difference approach to a graphene ribbon with zigzag termination. We reproduced [1] spectra and wavefunctions including localized edge states consistent with effective mass modulations generated by irradiation. By enabling efficient parameterization of the light field and system size as well as evaluation of the local density of states, this method offers a foundation for future studies of engineered Dirac systems.

[1]: De Martino, A., Dell’Anna, L., Handt, L., Miserocchi, A., and Egger, R. Two-Dimensional Dirac Fermions in a Mass Superlattice. Physical Review B 107, 115420 (2023).