Determination of kappa-1(T) and kappa-2(T) for Type Two Superconductors with Arbitrary Impurity Concentration

摘要

Formulas are derived for the constants kappa-1 and kappa-2 of superconducting alloys for arbitrary temperatures and impurity concentrations. Beginning with Gorkov's equations in matrix-form, the free energy density is calculated using Abrikosov's assumption of a fluxoid lattice. The impurities are treated by the usual averaging technique, retaining only s-and p-scattering, and a special technique is developed to treat exactly the non-vanishing commutator of different components of the gauge invariant derivative. The results contain the already known limiting cases. Intermediate values are obtained by performing machine calculations using the general formulas developed here. It is found that the values of kappa-1 and kappa-2 drop relatively strongly even for small impurity concentration, and also depend unexpectedly strongly on the ratio of sand p-scattering. The recent result of Cyrot, Caroli and de Gennes is confirmed according to which kappa-2 is approximately equal to kappa-1 in the firty limit. (Author)