Superconductivity in the antiferromagnetic quantum critical metal in two dimensions

To understand the interplay between non-fermi liquid behaviours and the onset of superconductivity in quantum critical metals, one has to understand the dynamics of electrons that are subject to both singular interactions mediated by gapless collective modes and large-angle scatterings caused by superconducting fluctuations. For this purpose, the patch theory that includes only a small portion of Fermi surface is insufficient. We develop a field theoretic functional renormalization group formalism for full low-energy effective field theories of non-Fermi liquids that include all gapless modes around the Fermi surface. Applying this formalism to the non-fermi liquid that arises at the antiferromagnetic quantum critical metal in two dimensions, we explain how critical spin fluctuations cause electrons to lose coherence on the one hand and at the same time drive superconductivity by providing an attractive glue for pairing.