Effect of the long-range Coulomb interaction on phase diagram of the Kohn-Luttinger superconducting state in idealized graphene

TL;DR

This paper investigates how long-range Coulomb interactions influence the phase diagram and critical temperature of Kohn-Luttinger superconductivity in idealized doped graphene, revealing significant qualitative changes.

Contribution

It demonstrates that including intersite Coulomb interactions qualitatively alters the phase diagram and increases the critical temperature of superconductivity in doped graphene.

Findings

Coulomb interactions significantly affect the competition between different superconducting symmetries.

Accounting for intersite Coulomb repulsion changes the phase diagram qualitatively.

Inclusion of Coulomb interactions enhances the critical superconducting temperature.

Abstract

The effect of the long-range Coulomb interaction on the realization of the Kohn-Luttinger superconductivity in idealized monolayer doped graphene is studied. 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 the intersite Coulomb interaction significantly affects the competition between the superconducting phases with the $f$-wave, $p+ip$-wave and $d + id$-wave symmetries of the order parameter. It is shown that the account for the Coulomb repulsion of electrons located at the next-nearest neighboring atoms in such a system changes qualitatively the phase diagram and enhances the critical superconducting temperature.