Superconductors containing impurities with crystal-field split energy levels

We investigate theoretically the problem of a superconducting matrix containing paramagnetic rare earth impurities with crystal-field split energy levels. There are two competing mechanisms which change the superconducting transition temperatureT _c. One is inelastic charge scattering of conduction electrons from the aspherical part of the 4f charge distribution, which leads to an increase inT _c similar to that of optical phonons. The other and often predominant mechanism comes from the exchange interaction, which depressesT _c and can be very effective even among non-magnetic levels via off-diagonal matrix elements. Crystalline fields serve to alter the effectiveness of the two kinds of scattering depending upon the symmetry character of the low-lying levels, and in favorable cases one may study separately the effects of the two types of scattering by adding different impurities to a given host. We find that crystal-field levels at energies quite high compared tok _B·T_c can still have an important effect onT _c. It is shown that the crystalline-field splitting should be directly observable as structure in the tunneling characteristics.