Pairing from Dynamically Screened Coulomb Repulsion in Bismuth
Recently, Prakash et. al. have discovered bulk superconductivity in single crystals of bismuth, which is a semi metal with extremely low carrier density. At such low density, we argue that conventional electron-phonon coupling is too weak to be responsible for the binding of electrons into Cooper pairs. We study a dynamically screened Coulomb interaction with effective attraction generated on the scale of the collective plasma modes. We model the electronic states in bismuth to include three Dirac pockets with high velocity and one hole pocket with a significantly smaller velocity. We find that at weak coupling the presence of a hole pocket greatly enhances the transition temperature. We show that this enhancement is mainly due to the static screening of the hole band and not due to the acoustic plasma mode. As a byproduct of studying superconductivity in a Dirac semi metal we find that Anderson's theorem is violated in the relativistic limit.