Plasma Excitations of Dressed Dirac Electrons in Graphene

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 $\epsilon_g$ between the conductance and valence bands. The value of $\epsilon_g$ may be adjusted by varying the frequency and intensity of the light which could be sizable compared to that which is generated by spin-orbit coupling or sub-lattice symmetry breaking. We present numerical results for the dispersion relation for plasma excitations for various energy gaps and separation between graphene layers. The induced $\epsilon_g$ opens up a gap in the particle-hole continuum thus allowing plasmon excitations of short wave-length. An optical and acoustic phonon-like modes are obtained in the double layer configuration. Those are very sensative to the induced energy gap and symmtry breaking between the layers.