A model of marginal Fermi liquid superconductor at two dimensions

In this paper we study a model of s-wave marginal Fermi liquid superconductor at two dimensions. Besides the usual Bardeen-Cooper-Schrieffer(BCS) point attractive interaction, the fermions in our system also interact {\em via} a long range repulsive interaction $v(q)=g_{D}/q^2$. We find that although superconductivity is not destroyed by the long-ranged repulsion interaction (demonstrated by the existence of Meissner effect), nevertheless the BCS pairing function $\Delta_{BCS}$ is strongly suppressed resulting in power-law correlation $<\Delta_{BCS}(\vec{x})\Delta_{BCS}(0)>\sim|\vec{x}|^{-2\gamma}$. This observation is explained within a general picture of marginal Fermi liquid.