Impurity Dependence of the Critical Field in Anisotropic Superconductors

Abstract

The effect of anisotropy of the superconducting energy-gap parameter upon the critical field $H_c$ when nonmagnetic impurities are present is theoretically examined. Gap anisotropy is shown to produce corrections, of the order of the mean-squared anisotropy $〈a^2〉$, to the isotropic-gap values of $H_c$. 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 $\frac{H_0^{}{}_{}{}^2}{8\pi \gamma T_c^{}{}_{}{}^2}$ and in the curve of $h=\frac{H_c}{H_0}$ vs $t=\frac{T}{T_c}$ results when impurities are added to an anisotropic, moderately weak-coupling superconductor. Expressions for these shifts are given.