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

Abstract

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. Application of this theory to anisotropy effects, with the clean limit taken in most cases, have been published elsewhere and additional studies will appear in the near future. In this paper we concentrate 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. When this is done we find that spin-orbit scattering is actually less effective in reducing paramagnetic limiting.p- andd-wave scattering have a marked effect on the upper critical fieldHc2 at low reduced temperatures, partially cancelling each other.d-wave scattering raisesHc2(O), but for physically acceptable parameter value is not sufficient to explain the apparent absence of paramagnetic limiting in some high-field superconductors. 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. The greatest problem remaining in our quest for a complete understanding of the upper critical field appears to be an accurate determination of the relevant normal state properties.