Enhancement of superconductivity near a nematic quantum critical point

TL;DR

This paper investigates how proximity to a nematic quantum critical point enhances superconductivity in low-temperature metals, showing that fluctuations boost T_c without altering pairing symmetry, with dimensionality affecting the enhancement strength.

Contribution

It demonstrates that nematic fluctuations can enhance superconducting T_c across different pairing symmetries, with a detailed analysis of the validity of BCS-Eliashberg theory near the NQCP.

Findings

T_c is enhanced by nematic fluctuations in all pairing channels.

The validity of BCS-Eliashberg theory extends outside a narrow critical region.

Dimensionality influences the magnitude of T_c enhancement, stronger in 2D than in 3D.

Abstract

We consider a low $T_c$ metallic superconductor weakly coupled to the soft fluctuations associated with proximity to a nematic quantum critical point (NQCP). We show that: 1) a BCS-Eliashberg treatment remains valid outside of a parametrically narrow interval about the NQCP; 2) the symmetry of the superconducting state (d-wave, s-wave, p-wave) is typically determined by the non-critical interactions, but $T_c$ is enhanced by the nematic fluctuations in all channels; 3) in 2D, this enhancement grows upon approach to criticality up to the point at which the weak coupling approach breaks-down, but in 3D the enhancement is much weaker.