Enhancement of Superconductivity near a Nematic Quantum Critical Point

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 noncritical interactions, but ${T}_{c}$ is enhanced by the nematic fluctuations in all channels, and (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.