Density-fluctuation-mediated superconductivity

We compare predictions of the mean-field theory of superconductivity for metallic systems on the border of a density instability for cubic and tetragonal lattices. The calculations are based on the parameterization of an effective interaction arising from the exchange of density fluctuations and assume that a single band is relevant for superconductivity. The results show that for comparable model parameters, density-fluctuation-mediated pairing is more robust in quasi-two dimensions than in three dimensions, and that the robustness of pairing increases gradually as one goes from a cubic structure to a more and more anisotropic tetragonal structure. We also find that the robustness of density-fluctuation-mediated pairing can depend sensitively on the incipient ordering wave vector. We discuss the similarities and differences between the mean-field theories of superconductivity for density mediated and magnetically mediated pairing.