On superconducting instability in non-Fermi liquid: scaling approach

Abstract

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 $A(\Lambda k,\Lambda \omega )={\Lambda }^{\alpha }A(k,\omega )$ it is shown that the pair susceptibility is also a scaling function of temperature with power defined by $\alpha$. We find three different regimes depending on the scaling constant. The BCS result is recovered for $\alpha =-1$ and it corresponds to a marginal scaling of the coupling constant. For $\alpha >-1$ the superconducting transition happens above some critical coupling. In the opposite case of $\alpha <-1$ 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 the interlayer Josephson tunneling are discussed. 1 ps file for fig is attached at the bottom of the tex file.

10 pages + 1 fig, LA-UR-2756

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