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Plasma excitations of dressed Dirac electrons in graphene layers

The dispersion relation for the collective plasma excitations of optically dressed Dirac electrons in single and double graphene layers is calculated in the random-phase approximation. The presence of circularly polarized light gives rise to an energy gap $E_g$ between the conduction and valence energy bands. The value of $E_g$ may be adjusted by varying the frequency and intensity of the light and could be much larger compared to that which is generated by spin-orbit coupling, and may reach values of the gap reported for epitaxially grown graphene. We report plasmon dispersion relations for various energy gaps and separation between graphene layers. For a single graphene sheet, we find that plasmon modes may be excited for larger wave vector and frequency when subjected to light. For double layers, we obtained an optical and phonon-like mode and found that the optical mode is not as sensitive as the phonon-like mode in the long wavelength limit when the layer separation is varied, for a chosen $E_g$. Contrary to the notion that the effective mass acquired by Dirac electrons provides a crossover to two-dimensional electron gas (2DEG) behavior, we found that the response of dressed Dirac electrons to an external perturbation is governed by the Dirac cone $ω= v_F q$, where $_F$ is the Fermi velocity and $q$ is the wave vector. Consequently, the dressed electron plasma although massive still has Dirac origin giving rise to differences in the properties of the plasmon modes compared with those for the 2DEG.