The Kohn-Luttinger superconductivity in idealized doped graphene

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.

arXiv comment9 pages, 5 figures

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• Unconventional superconductivity in low density electron systems and conventional superconductivity in hydrogen metallic alloys under pressure
• The Kohn-Luttinger effect and anomalous pairing in new superconducting systems and graphene
• Electronic Structure and Kohn-Luttinger Superconductivity of Heavily-Doped Single-Layer Graphene
• A Hybrid-Monte-Carlo study of monolayer graphene with partially screened Coulomb interactions at finite spin density
• Phase diagram of the Kohn-Luttinger superconducting state for bilayer graphene
• Kohn-Luttinger superconductivity in monolayer and bilayer semimetals with the Dirac spectrum
• Anomalous superconductivity and superfluidity in repulsive fermion systems
• Renormalization-group approach to the Kohn-Luttinger superconductivity: Amplification of the pairing gap from ${\ell }^4$ to $\ell$
• Effect of the long-range Coulomb interaction on phase diagram of the Kohn-Luttinger superconducting state in idealized graphene
• Pairing around a Single Dirac Point: A Unifying View of Kohn-Luttinger Superconductivity in Chern Bands, Quarter Metals, and Topological Surface States