Effect of the Long-Range Coulomb Interaction on the Phase Diagram of the Kohn–Luttinger Superconducting State in Idealized Graphene

The effect of the long-range Coulomb interaction on the formation of the Kohn–Luttinger superconductivity in monolayer doped graphene is studied disregarding the Van der Waals potential of the substrate and both magnetic and non-magnetic impurities. It is shown that the allowance for the Kohn–Luttinger renormalizations up to the second order in perturbation theory in the on-site Hubbard interaction inclusively, as well as in the intersite Coulomb interaction, significantly affects the interplay between the superconducting phases with the f-wave, \(p+ip\)-wave, and \(d + id\)-wave symmetries of the order parameter. It is demonstrated that taking Coulomb repulsion of electrons located at the next-nearest neighboring atoms in such a system into account changes qualitatively the phase diagram and enhances the critical temperature of the transition to the superconducting phase.