B-doped diamond: Superconductivity without Fermi surface

We consider superconductivity in boron (B) doped diamond using a simplified model for the valence band of diamond. We treat the substitutional disorder of B ions by the coherent potential approximation and the attractive force between holes by the ladder approximation under the assumption of instantaneous interaction. We thereby calculate the quasiparticle life time, the evolution of the single-particle spectra due to doping, and the effect of disorder on the critical temperature Tc. We in particular compare our results with those for supercell calculations to see the role of disorder, which turns out to be of crucial importance.