Magnetic impurity effect on superconductivity in systems with comparable Fermi and Debye energies

Abstract

We obtain the basic system of equations for a superconductivity theory of a system with a chaotically distributed paramagnetic substitution impurity in which the Migdal theorem is violated (the condition ωD ≪EF cannot be assumed). The electron-phonon and impurity diagrams and also the additional diagrams corresponding to intersections of the electron-phonon and electron-impurity lines are taken into account. In the weak electron-phonon coupling limit, we obtain an equation for the superconducting transition temperature TC that differs from the corresponding equation for the usual superconductors by renormalizations of TC0 and of the impurity scattering parameter, ρ. These quantities depend essentially on the Migdal parameter ωD/EF and on the transferred momentum qc. We show that the decrease of TC with the increase of the impurity concentration is slowed, as compared with usual superconductors, to an extent determined by m and qc. We also evaluate the isotopic coefficient α, whose behavior as a function of the impurity concentration depends on m and qc.