Solutions of the Eliashberg equations with abnormally large values of 2Δ(0)/T_c

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