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.

9 pages, 5 figures

References in corpus (7)

• The electronic properties of graphene
• Bipolar supercurrent in graphene
• Superconductivity in the repulsive Hubbard model: an asymptotically exact weak-coupling solution
• Density waves and Cooper pairing on the honeycomb lattice
• Kohn-Luttinger superconductivity in graphene
• Pomeranchuk instability in doped graphene
• Effect of long-range interactions on the Kohn-Luttinger mechanism of the Cooper instability in the Shubin-Vonsowsky model

Cited by in corpus (7)

• Functional Renormalization Group Study of Superconductivity in Rhombohedral Trilayer Graphene
• Fermi-Bose mixtures and BCS-BEC crossover in high-Tc superconductors
• 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
• Kohn-Luttinger superconductivity in monolayer and bilayer semimetals with the Dirac spectrum
• Renormalization-group approach to the Kohn-Luttinger superconductivity: Amplification of the pairing gap from ${\ell }^4$ to $\ell$
• Pairing around a Single Dirac Point: A Unifying View of Kohn-Luttinger Superconductivity in Chern Bands, Quarter Metals, and Topological Surface States