Superconducting instability in non-Fermi liquids

TL;DR

This paper investigates the emergence of superconductivity in non-Fermi liquids near quantum critical points, using RG analysis to identify fixed points and showing that superconductivity is favored over non-Fermi liquid behavior in key physical cases.

Contribution

It introduces a controlled RG framework for analyzing superconductivity in non-Fermi liquids with critical Fermi surfaces of arbitrary dimensions.

Findings

Superconductivity is preemptive in key physical cases of (d=3, m=2) and (d=2, m=1).

Order parameter fluctuations strongly enhance superconductivity at quantum critical points.

The formalism identifies fixed points and flow equations for systems with critical Fermi surfaces.

Abstract

We use renormalization group (RG) analysis and dimensional regularization techniques to study potential superconductivity-inducing four-fermion interactions in systems with critical Fermi surfaces of general dimensions ($m$) and co-dimensions ($d-m$), arising as a result of quasiparticle interaction with a gapless Ising-nematic order parameter. These are examples of non-Fermi liquid states in $d$ spatial dimensions. Our formalism allows us to treat the corresponding zero-temperature low-energy effective theory in a controlled approximation close to the upper critical dimension $d=d_c(m)$. The fixed points are identified from the RG flow equations, as functions of $d$ and $m$. We find that the flow towards the non-Fermi liquid fixed point is preempted by Cooper pair formation for both the physical cases of $(d=3, m=2)$ and $(d=2, m=1)$. In fact, there is a strong enhancement of superconductivity by the order parameter fluctuations at the quantum critical point.