On superconducting instability in non-Fermi liquid: scaling approach

TL;DR

This paper investigates superconducting instability in non-Fermi liquids using a scaling approach, identifying different regimes based on spectral function scaling and implications for high-$T_c$ superconductors.

Contribution

It introduces a scaling framework to analyze superconducting transitions in non-Fermi liquids, revealing new regimes and conditions for transition based on spectral function scaling.

Findings

Recovering BCS result at $ extalpha = -1$

Superconducting transition above critical coupling for $ extalpha > -1$

Transition at low temperatures for $ extalpha < -1$

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.