Upper critical field of superconducting anisotropic polycrystals

We present a theory of the upper critical field for an anisotropic polycrystal. This theory is based on the well-known separable model for the electron-phonon anisotropy which is expanded to describe the Fermi-velocity anisotropy. It is assumed to be sufficient to describe these anisotropies by the mean-square parameters 〈$a^2$〉 and 〈$b^2$〉, respectively. Comparison with existing N-band models shows that our model only allows formation of Cooper pairs from quasiparticles which belong to the same Fermi-surface sheet. Predictions of this theory are discussed using a model system emphasizing the deviation of the upper critical field of the anisotropic system from an equivalent isotropic one. Finally, a procedure is suggested which should enable experimentalists to make a more detailed analysis of experimental data in terms of anisotropy effects.