Superconducting instability in a non-Fermi liquid scaling approach

The superconducting instability in a non-Fermi liquid in dimensions d > 1 is considered. For a particular form of the single particle spectral function with homogeneous scaling A(λk, λ ω) = λα A(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. Bardeen-Cooper-Schrieffer 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-T c with a superconducting transition driven by interlayer Josephson tunnelling are discussed.