Kohn-Luttinger superconductivity in monolayer and bilayer semimetals with the Dirac spectrum

TL;DR

This paper investigates how Coulomb interactions influence superconductivity in monolayer and bilayer graphene with Dirac spectra, revealing that interlayer interactions can significantly enhance the transition temperature.

Contribution

It introduces a detailed analysis of Coulomb interactions and their impact on superconducting pairing symmetries in doped graphene using the Kohn-Luttinger mechanism.

Findings

Superconducting transition temperature is higher in bilayer graphene with interlayer Coulomb interactions.

Interlayer Coulomb interactions affect the competition between f-wave and d+id-wave pairing symmetries.

Kohn-Luttinger renormalizations significantly influence the effective pairing interactions.

Abstract

The effect of Coulomb interaction in an ensemble of Dirac fermions on the formation of superconducting pairing in monolayer and bilayer doped graphene is studied using the Kohn-Luttinger mechanism disregarding the Van der Waals potential of the substrate and impurities. The electronic structure of graphene is described using the Shubin-Vonsovsky model taking into account the intratomic, interatomic, and interlayer (in the case of bilayer graphene) Coulomb interactions between electrons. The Cooper instability is determined by solving the Bethe-Saltpeter integral equation. The renormalized scattering amplitude is obtained with allowance for the Kohn-Luttinger polarization contributions up to the second order of perturbation theory in the Coulomb interaction. It plays the role of effective interaction in the Bethe-Salpeter integral equation. It is shown that the allowance for the Kohn-Luttinger renormalizations as well as intersite Coulomb interaction noticeably affects the competition between the superconducting phases with the $f-$wave and $d + id-$wave symmetries of the order parameter. It is demonstrated that the superconducting transition temperature for an idealized graphene bilayer with significant interlayer Coulomb interaction between electrons is noticeably higher than in the monolayer case.