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 via a long range repulsive interaction v(q) = gD/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 ∆BCS is strongly suppressed resulting in power-law correlation < ∆BCS(~x)∆BCS(0) >∼ |~x| −2γ . This observation is explained within a general picture of marginal Fermi liquid. 71.10.Hf,74.20.-z,74.25.-q Typeset using REVTEX 1 Since the discovery of high-Tc superconductors, there has been enormous interests in the study of non-Fermi liquid theories in two dimensions [1–3]. The normal state of high-Tc superconductors shows rich physical behaviors which seems to deviate from usual Landau Fermi liquid theory predictions. For example, in the optimally doped regime, resistivity shows a linear temperature dependence, whereas in underdoped regime, the resistivity shows a power-law temperature dependence, and with a pseudo-gap in low energy excitation spectrum. Although there exists a lot of theoretical studies on microscopic theories of non-Fermi liquid normal states, at present there exists very few systematic investigation into how the superconducting state is affected by non-Fermi liquid behaviours. In this paper we study a microscopic model of s-wave marginal Fermi liquid superconductor at two dimensions. The Hamiltonian of our model consists of two parts, H = Hmfl +HBCS , where Hmfl = ∑ ~k,σ ǫ(k)ψ σ( ~k)ψσ(~k) + 1 2L2 ∑ |~ q|≤qc v(q)ρ(~q)ρ(−~q), (1a)