Properties of anisotropic superconductors with approximately neutral electron-electron interaction

A Bardeen-Cooper-Schrieffer-type theory of superconductivity, in which the attractive electron-electron interaction is represented by a separable anisotropic term and the repulsion by an isotropic term, is extended to calculations of a variety of properties of the pure material and of the effects of both normal and paramagnetic impurities on the transition temperature, $T_c$. The goals are (1) the identification of properties which are likely to be quite different for materials with an approximately neutral interaction as compared with the usual regime in which the attraction dominates and (2) the estimation of maximum impurity concentrations which can be tolerated. For the pure material, the main conclusions are that the mean-squared anisotropy of the energy gap, the ratios of twice the Fermi-surface average of the gap to $T_c$, and of the zero-temperature critical magnetic field, $H_c\mathrm{}\left(0\right)\mathrm{}$, to $T_c$, the jump in the specific heat at $T_c$, the isotope effect, and the quasiparticle density of states can all be quite different, whereas the reduced temperature-dependent quantities $\frac{{\Delta }_{\overrightarrow{\mathrm{k}}}\mathrm{}\left(t\right)\mathrm{}}{{\Delta }_{\overrightarrow{\mathrm{k}}}\mathrm{}\left(0\right)\mathrm{}}$ and $\frac{H_c\mathrm{}\left(t\right)\mathrm{}}{H_c\mathrm{}\left(0\right)\mathrm{}}$ are not. Although very sensitive to the value of the meansquared anisotropy, it is estimated that the maximum tolerable concentrations of both kinds of impurities are on the order of ${10}^{-2\mathrm{}}$% to ${10}^{-4\mathrm{}}$%.