Condensed Matter Seminar - Steven Kivelson (Stanford)
Enhancement of superconductivity near a nematic quantum critical point
Two topics that have attracted intense theoretical study over the past decade are the nature of quantum critical phenomena in metallic systems and what, if anything, such critical points have to do with an unconventional mechanism of superconducting pairing. The still un-mastered subtleties of the first problem have precluded convincing resolution of the second. For the model problem of a weakly interacting metal in proximity to a nematic quantum critical point (NQCP), we identify a broad regime of parameters in which the nature of the induced superconductivity can be understood in a theoretically well controlled manner without needing to resolve the deep, unsolved issues of metallic criticality. 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 Tc 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.