Metallic quantum critical points with finite BCS couplings

TL;DR

This paper investigates how superconductivity behaves near metallic quantum critical points, revealing a non-Fermi liquid state with finite BCS coupling where fluctuations are strong but superconductivity does not dominate.

Contribution

It introduces a novel non-Fermi liquid fixed point with finite BCS coupling at metallic quantum critical points, balancing pairing tendencies and quasiparticle destruction.

Findings

Existence of a non-Fermi liquid fixed point with finite BCS coupling.

Superconducting fluctuations are significant but do not lead to superconductivity.

The fixed point connects continuously to the superconducting regime.

Abstract

We study the fate of superconductivity in the vicinity of a class of metallic quantum critical points obtained by coupling a Fermi surface to a critical boson. In such systems there is a competition between the enhanced pairing tendency due to the presence of long-range attractive interactions near criticality, and the suppression of superconductivity due to the destruction of the Landau quasiparticles. We show that there are regimes in which these two effects offset one another, resulting in a novel non-Fermi liquid fixed point with finite, scale invariant, BCS coupling. While these interactions lead to substantial superconducting fluctuations, they do not drive the system into a superconducting ground state. The metallic quantum critical fixed points are connected to the superconducting regime by a continuous phase transition. These results are established using a controlled expansion in the deviation from d=3 spatial dimensions, as well as in a large number N of internal flavors. We discuss the possible relevance of our findings to the phenomenon of superconducting domes condensing out of a non-Fermi liquid normal state near quantum critical points.