THE EFFECT OF RESONANCE SCATTERING ON THE CRITICAL TEMPERATURE OF ANISOTROPIC SUPERCONDUCTORS

In a previous paper, the effect of a nonmagnetic resonant d orbital (bound to a transition-metal impurity) on a simple isotropic superconductor was discussed. It was shown that the critical temperature Te of such an alloy suffered an initial linear decrease proportional to the impurity concentration NI. The resulting curve of Te versus NI remains linear for experimentally realizable values of the impurity concentration. However, this is not borne out experimentally and one reason for the discrepancy is that the anisotropy of the superconductor was not taken into account theoretically. In this paper, it is shown that the change in Te due to the presence of nonmagnetic transition-metal impurities is given by the sum of three terms, as follows: (a) the isotropic term due to the interaction of the d orbital with the conduction electrons found in the previous paper, (b) the usual term due to the "anisotropic effect" of Markowitz and Kadanoff (1963), and (c) a cross term between the resonance scattering and the anisotropic scattering. The term (c) is shown to be very small compared with (a) and (b) and hence the procedure for comparison with experiment used by Boato et al. (1966) is justified in our approximation.