ON THE UPPER CRITICAL-FIELD OF ANISOTROPIC SUPERCONDUCTORS

We study in general the upper critical field (B(c2)(T)) for models describing clean, weak-coupling superconductors which are isotropic perpendicular to the magnetic field. Our considerations are based on generalized WHH-equations explicitly taking into account a nontrivial spatial behaviour of the electrons' pairing interaction and an energy dependence of the electronic density of states. A simple formula for the slope dB(c2)(T)/dT\T = T(c) is derived. Moreover it is shown by analytical means that the generalized WHH-B(c2)(T)-equations can be simplified in a very good approximation to an "universal" equation for the reduced upper critical field b(c2)*(t) (t = T/T(c)) depending solely on the shape of the Fermi surface, and the error in this approximation is estimated. We calculate explicit formulas for the series expansions of b(c2)*(t) in (1 - t) greater-than-or-equal-to 0 and t greater-than-or-equal-to 0 up to order 4 and 2, respectively. Finally we apply our results to a model with an "hour-glass" shaped Fermi surface describing layered superconductors with the magnetic field perpendicular to the layers.