Plasmonic Cooper pairing in single layer graphene

The dielectric function method (DFM), which uses a non-adiabatic approach to calculate the critical temperatures for superconductivity, has been quite successful in describing superconductors at low carrier densities. This regime of carrier densities causes other theories, such as BCS and Migdal-Eliashberg theory, to violate their assumption of a small Debye window. We investigate the application of DFM to the linear dispersion of single layer graphene. We derive the gap equation of DFM for a Dirac cone and calculate the critical temperature as a function of carrier density. This is done using an interaction potential that utilizes the Random Phase Approximation dielectric function and thus allows for plasmonic interactions. Our results show a significantly different behaviour of the critical temperature as a function of carrier density when compared to the BCS result. Thus, we find the DFM approach to be better suited when considering graphene systems at low carrier densities.