Enhanced pairing of quantum critical metals near d=3+1

Abstract

We study the dynamics of a quantum critical boson coupled to a Fermi surface in intermediate energy regimes where the Landau damping of the boson can be parametrically controlled, either via large Fermi velocity or by large-N techniques. We develop a systematic approach to the BCS instability of such systems, including careful treatment of the enhanced log2 and log3 singularities which appear already at 1-loop. These singularities arise due to the exchange of a critical boson in the Cooper channel and are absent in Fermi liquid theory. We also treat possible instabilities to charge density wave (CDW) formation, and compare the scales BCS and CDW of the onset of the instabilities in different parametric regimes. We address the question of whether the dressing of the fermions into a non-Fermi liquid via interactions with the order parameter field can happen at energies >BCS,CDW.