ar X iv : c on d - m at / 0 30 95 51 v 1 2 4 Se p 20 03 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 parameterisation 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 ro-bustness 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 wavevector. We discuss the similarities and differences bewteen the mean-field theories of superconductivity for density mediated and magnetically mediated pairing.