Electron-electron interactions in graphene sheets

The effects of the electron-electron interactions in a graphene layer are investigated. It is shown that short-range couplings are irrelevant and scale towards zero at low energies, due to the vanishing of density of states at the Fermi level. Topological disorder enhances the density of states and can lead to instabilities. In the presence of sufficiently strong repulsive interactions, p-wave superconductivity can emerge.