BCS Superconductivity in Quantum Critical Metals

TL;DR

This paper reformulates BCS theory as a scaling theory to better understand superconductivity in quantum critical metals, showing enhanced transition temperatures under certain conditions.

Contribution

It introduces a scaling framework for BCS theory applicable to quantum critical metals, extending beyond conventional superconductors.

Findings

Superconducting Tc is strongly enhanced with strong retardation and weak coupling.

The scaling theory aligns well with observed properties near quantum critical points.

The approach generalizes BCS theory to non-traditional, quantum critical systems.

Abstract

Departing from the assumption that pairing is induced by an retarded external 'bosonic glue', we reformulate the Bardeen-Cooper-Schrieffer theory of superconductivity as a scaling theory. Conventional superconductors correspond with the asymptotically free case but the theory can be effortlessly generalized to handle quantum critical metals. We find that superconducting Tc's are strongly enhanced in the latter when retardation is strong while the coupling is weak. It appears that this simple scaling theory does account quite well for superconducting properties near quantum critical points.