Inhibition of the Fermi velocity renormalization in a graphene sheet by the presence of a conducting plate

We investigate the renormalization of the Fermi velocity in a plane graphene sheet in the presence of a parallel conducting plate. We use the pseudo-quantum electrodynamics to describe the Coulombian interaction between the electrons, but taking into account that this interaction is changed by the conducting plate. Incorporating the influence of the plate into the gauge field, we obtain the correspondent photon propagator and electron self-energy, showing that the logarithmic renormalization of the Fermi velocity is inhibited by the presence of the plate. Our result may be useful as an alternative way to control the electronic properties of graphene.