Phonon-mediated electron pairing in graphene

TL;DR

This paper investigates the potential for phonon-mediated superconductivity in doped graphene, analyzing how different phonon modes and electron pairing symmetries influence the pairing mechanism and resulting order parameter structures.

Contribution

It provides a detailed theoretical analysis of electron pairing in doped graphene considering both in-plane and out-of-plane phonons, including quadratic coupling effects and complex order parameter structures.

Findings

Unconventional orbital-spin symmetry of the pairing order parameter.

Sign and magnitude of phonon contributions depend on phonon mode symmetry.

Multiple possible structures of the superconducting order parameter.

Abstract

The possibility of superconducting pairing of electrons in doped graphene due to in-plane and out-of-plane phonons is studied. Quadratic coupling of electrons with out-of-plane phonons is considered in details, taking into account both deformation potential and bond-stretch contributions. The order parameter of electron-electron pairing can have different structures due to four-component spinor character of electrons wave function. We consider s-wave pairing, diagonal on conduction and valence bands, but having arbitrary structure with respect to valley degree of freedom. The sign and magnitude of contribution of each phonon mode to effective electron-electron interaction turns out to depend on both the symmetry of phonon mode and the structure of the order parameter. Unconventional orbital-spin symmetry of the order parameter is found.