Effect of interaction anisotropy on the superconducting transition temperature

We study the influence of pairing interaction anisotropy on the superconducting transition temperature Tc. Our approach involves examining the normal-state instability to Cooper-pair formation using the Bethe-Salpeter equation within a number of simplifying approximations. We make a detailed study of some simple models and find that anisotropy (regardless of its relative strength) has always the effect of increasing Tc. We then consider the generality of this result and find that a general theorem ensures that it holds under rather nonrestrictive assumptions. We discuss the possible implications of our results for superconductivity in real anisotropic materials such as high-temperature superconductors.