Abstract

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/| (the -model). This model describes, in particular, pairing at a 2D Ising-nematic critical point (=1/3) and at a 2D antiferromagnetic critical point (=1/2) and pairing by an Einstein phonon with vanishing dressed Debye frequency (=2). I argue that in all cases pairing wins over non-Fermi liquid, 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 discuss how non-BCS pairing affects the gap structure on the real frequency axis and the superconducting stiffness.