Solutions of the Eliashber equations with abnormally large values of 2Δ(0)/Tc

The authors consider the Eliashberg equations with an electron-phonon matrix element g(k, k', q) possessing a low-energy cutoff ξ1. In the superconducting state, the authors assume that this cutoff is bound from below by the superconducting gap 2Δ. They solve for Δ and ξ1 self-consistently, as a function of temperature, and find that the ratio 2Δ(0)/Tc is very large; for parameters that the authors consider realistic for the cuprates, this ratio is approximately 10. This calculation applies to materials where the mean free path is long (clean limit). The authors also find that a hysteretic behavior is in principle possible