Impurity Dependence of the Critical Field in Anisotropic Superconductors

The effect of anisotropy of the superconducting energy-gap parameter upon the critical field Hc when nonmagnetic impurities are present is theoretically examined. Gap anisotropy is shown to produce corrections, of the order of the mean-squared anisotropy 〈a²〉, to the isotropic-gap values of Hc. With an anisotropic BCS-like model introduced by Markowitz and Kadanoff, the reduction of these corrections as impurities are added is calculated. An upward shift in the value of H₀^_²8πγTc^_² and in the curve of h=HcH₀ vs t=TTc results when impurities are added to an anisotropic, moderately weak-coupling superconductor. Expressions for these shifts are given.