Superconductivity in Graphene Stacks

Superconductivity in twisted and untwisted graphene stacks is investigated. The role of the screened long range repulsive Coulomb interaction in the superconducting pairing is studied in detail, as it is the largest electron-electron interaction in twisted bilayers. Screening includes electron-hole excitations, plasmons, and longitudinal acoustic phonons, all included via the RPA dielectric function. A significant contribution to pairing in twisted bilayer graphene comes from moiré assisted processes. Superconductivity in fully spin and valley polarized systems is also studied.

The long range Coulomb interaction reasonably describes observed trends in superconducting graphene stacks. It marks a significant difference between a twisted graphene bilayer and other moiré systems, such as twisted double bilayers, and helical trilayers. Pairing in untwisted bilayers and trilayers is weaker than in twisted bilayer graphene.

The superconducting order parameter in twisted bilayer graphene can be f-wave like, that is, there are full gaps with opposite signs in the two valleys. The superconducting order parameter in other graphene stacks usually shows nodes at the Fermi surface.