The Kohn-Luttinger superconductivity in idealized doped graphene

TL;DR

This paper investigates how long-range Coulomb interactions influence the emergence of superconductivity in idealized doped graphene, revealing the impact on various unconventional pairing symmetries using the Kohn-Luttinger mechanism.

Contribution

It introduces a detailed analysis of superconducting phase diagrams in doped graphene considering second-order Coulomb repulsion effects within the Kohn-Luttinger framework.

Findings

Superconducting phases with f-, d+id-, and p+ip-wave symmetries are identified.

Intersite Coulomb repulsion significantly alters the phase diagram.

Kohn-Luttinger renormalizations impact the stability of different pairing symmetries.

Abstract

Idealized graphene monolayer is considered neglecting the van der Waals potential of the substrate and the role of the nonmagnetic impurities. The effect of the long-range Coulomb repulsion in an ensemble of Dirac fermions on the formation of the superconducting pairing in a monolayer is studied in the framework of the Kohn-Luttinger mechanism. The electronic structure of graphene is described in the strong coupling Wannier representation on the hexagonal lattice. We use the Shubin-Vonsowsky model which takes into account the intra- and intersite Coulomb repulsions of electrons. The Cooper instability is established by solving the Bethe-Salpeter integral equation, in which the role of the effective interaction is played by the renormalized scattering amplitude. The renormalized amplitude contains the Kohn-Luttinger polarization contributions up to and including the second-order terms in the Coulomb repulsion. We construct the superconductive phase diagram for the idealized graphene monolayer and show that the Kohn-Luttinger renormalizations and the intersite Coulomb repulsion significantly affect the interplay between the superconducting phases with $f-$, $d+id-$, and $p+ip-$wave symmetries of the order parameter.