Fermi velocity reduction in graphene due to enhanced vacuum fluctuations

It is well known that the confinement of matter inside a microcavity can significantly enhance the light-matter interactions. As a result the vacuum fluctuations, induced by virtual photons, can occur in a volume much lower than the free-space diffraction limit. In this work we show that, for a single doped graphene plane inside a microcavity, these enhanced vacuum interactions can produce a significant reduction in the Fermi velocity of the electrons. The effect arises because the energies of the photons are much larger than the energies of the electrons in graphene, which implies that the vacuum exchange interaction is repulsive around the Fermi level. Consequently the quasiparticle Fermi velocity decreases, in contrast with the enhancement obtained in Hartree-Fock. For THz cavities, the reduction is highly localized around the Fermi level, and is practically independent of the carrier density in graphene.