On superconducting instability in non-Fermi liquid: scaling approach

The superconducting instability in a non-Fermi liquid in d > 1 is considered. For a particular form of the single particle spectral function with homogeneous scaling A(Λk,Λω) = ΛA(k, ω) it is shown that the pair susceptibility is also a scaling function of temperature with power defined by α. We find three different regimes depending on the scaling constant. The BCS result is recovered for α = −1 and it corresponds to a marginal scaling of the coupling constant. For α > −1 the superconducting transition happens above some critical coupling. In the opposite case of α < −1 for any fixed coupling the system undergoes a transition at low temperatures. Possible implications for theories of high-Tc with a superconducting transition driven by the interlayer Josephson tunneling are discussed.