Phase diagram of the Kohn-Luttinger superconducting state for bilayer graphene

TL;DR

This paper investigates how intersite and interplane Coulomb interactions influence the Kohn-Luttinger superconductivity in bilayer doped graphene, revealing effects on phase boundaries, pairing symmetries, and critical temperature enhancement.

Contribution

It provides a detailed phase diagram of superconducting states considering long-range Coulomb interactions within an extended Hubbard model.

Findings

Interplane Coulomb interaction increases the critical temperature.

Long-range intraplane Coulomb interactions affect pairing symmetry competition.

Phase boundaries depend on Coulomb interaction strength and symmetry of the order parameter.

Abstract

The effect of the intersite and interplane Coulomb interactions between the Dirac fermions on the formation of the Kohn-Luttinger superconductivity in bilayer doped graphene is studied disregarding the effects of the van der Waals potential of the substrate and both magnetic and non-magnetic impurities. The phase diagram determining the boundaries of superconductive domains with different types of symmetry of the order parameter is built using the extended Hubbard model in the Born weak-coupling approximation with allowance for the intratomic, interatomic, and interlayer Coulomb interactions between electrons. It is shown that the Kohn-Luttinger polarization contributions up to the second order of perturbation theory in the Coulomb interaction inclusively and an account for the long-range intraplane Coulomb interactions significantly affect the competition between the superconducting $f-$, $p+ip-$, and $d+id-$wave pairings. It is demonstrated that the account for the interplane Coulomb interaction enhances the critical temperature of the transition to the superconducting phase.