Theory of Kondo Effect in Superconductors. I: Transition Temperature and Upper Critical Field

Abstract

An approximation is proposed for the magnetic-impurity effect on superconductivity, where the many-body effect of impurities, i.e., the Kondo effect, is fully taken into account. It is an interpolation between the behavior in two limiting cases; i.e., the pair-breaking effect due to magnetic scattering of electrons in the high-temperature and energy region, and the effective repulsive interaction between the Cooper-pair electrons mediated by virtual polarization of impurities in the low-temperature and energy region. Using this approximation, the superconducting transition temperature and the upper critical field are calculated in the presence of impurities. Contrary to the Muller-Hartmann-Zittartz theory, a finite critical concentration is obtained for any value of the Kondo temperature, though it increases rapidly when the Kondo temperature increases.