Interplay Between Superconductivity and Non-Fermi Liquid at a QCP in a Metal

I discuss the interplay between non-Fermi liquid behaviour and pairing near a quantum-critical point (QCP) in a metal. These tendencies are intertwined in the sense that both originate from the same interaction mediated by gapless fluctuations of a critical order parameter. The two tendencies compete because fermionic incoherence destroys the Cooper logarithm, while the pairing eliminates scattering at low energies and restores fermionic coherence. I discuss this physics for a class of models with an effective dynamical interaction V ? ~1/|?|^y (the y-model). This model describes, in particular, the pairing at a 2D Ising-nematic critical point (y=1/3), a 2D antiferromagnetic critical point (y=1/2) and the pairing by an Einstein phonon with vanishing dressed Debye frequency (y=2). I argue the pairing wins, unless the pairing component of the interaction is artificially reduced, but the pairing mechanism is fundamentally different from BCS and is associated with the emergence of complex exponents for the pairing susceptibility. I will further argue that there is a topological transition in the y-model, at y=2.