Quasi-classical theory of the upper critical field of high-field superconductors. Application to momentum-dependent scattering

A theory of the upper critical field is developed which is sufficiently general to incorporate strong coupling effects, anisotropy of both Fermi surface and pairing interaction, and momentum-dependent scattering, including exchange and spin-orbit scattering. It is not necessary to assume that spin-orbit scattering is a small fraction of the total scattering. An important improvement in this theory is the correct treatment of the spatial dependence of the anomalous Green function and the order parameter in the mixed state. In the presence of anisotropy this is, in general, not described with sufficient accuracy by the Abrikosov vortex lattice. This paper concentrates on the effects arising from the momentum dependence of the elastic scattering. If spin-orbit scattering forms a sizeable fraction of the total scattering, it is necessary to take its explicit momentum dependence into account. For a complete description of the upper critical field, other effects mentioned above need to be taken into account, but for superconductors of intermediate purity the momentum dependence of the scattering cannot be ignored. 85 refs.