A model of marginal Fermi liquid superconductor at two dimensions

Abstract

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 $Δ_{BCS}$ is strongly suppressed resulting in power-law correlation $<Δ_{BCS}(\vec{x})Δ_{BCS}(0)>\sim|\vec{x}|^{-2γ}$. This observation is explained within a general picture of marginal Fermi liquid.