Theory of the upper critical field in anisotropic superconductors

The upper critical field in superconductors is calculated using a model which incorporates anisotropy in both the Fermi surface and the superconducting pair state. The effects of nonlocality are included to all orders in perturbation theory, giving results valid over nearly the entire temperature range. It is shown that increasing Fermi-surface anisotropy causes $H_{c2\mathrm{}}$ to become more nearly linear in temperature, whereas even small amounts of pair-state anisotropy cause positive curvature in $H_{c2\mathrm{}}\mathrm{}\left(T\right)\mathrm{}$ near $T_{c0\mathrm{}}$. All effects of anisotropy are diminished by increasing the impurity scattering rate. The theory is fit to experimental data on Nb${\mathrm{Se}}_2$.