STRONG-COUPLING CORRECTIONS TO THE BARDEEN-COOPER-SCHRIEFFER RATIOS FOR A D-WAVE SUPERCONDUCTOR

We have calculated, for a d-wave superconductor, the strong-coupling corrections to the Bardeen-Cooper-Schrieffer (BCS) ratios: DELTAC(T(c))/gammaT(c),2DELTA0/T(c),gammaT(c)2/H(c)2(0),h(c)(0) as well as the ratios for the normalized slope in the specific-heat jump at T(c) and London penetration depth. We have used a step-function approximation for the gap function and considered an Einstein spectral density for the bosons. We have obtained terms up to 0 (T(c)4/omega(E)4) (here T(c)/omega(E) is the strong-coupling parameter and omega(E) is the Einstein energy). While our results are approximate for the strong-coupling cases, the weak-coupling results are exact. These weak-coupling ratios are no longer universal and depend on the d-wave considered. Our formulas are also applicable for some extended s-wave superconductors which have a basis function with a zero average over the Fermi surface.