The dielectric function method for superconducting materials

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 semi-phenomenological theory uses the dielectric function of the material to describe the inter-electron interaction and obtains very BCS-like equations for the superconducting gap and the critical temperature. However, DFM uses an interaction of arbitrary form, instead of a constant attraction in a Debye window as is the case for BCS. We investigate the application of DFM to the linear dispersion of single layer graphene. This is done using an interaction potential that uses the Random Phase Approximation dielectric function and thus allows for plasmonic interactions which are most relevant at low carrier doping.