Abstract:
I discuss the interplay between non-Fermi liquidbehaviour and pairing near a quantum-critical point (QCP) in a metal. These tendencies are intertwined in the sensethat both originate from the same interaction mediated by gapless fluctuationsof a critical order parameter. The twotendencies compete because fermionic incoherence destroys the Cooper logarithm,while the pairing eliminates scattering at low energies and restores fermioniccoherence. I discuss this physics for aclass of models with an effective dynamical interaction V (W) ~1/|W|g (theg-model). This model describes, in particular, thepairing at a 2D Ising-nematic critical point (g=1/3),a2D antiferromagnetic critical point (g=1/2)and the pairing by an Einstein phononwith vanishing dressed Debye frequency (g=2). I argue the pairing wins, unless the pairing componentof the interaction is artificially reduced, but because of fermionicincoherence in the normal state, the system develops pseudogap behaviour in thetemperature range between the onset of the pairing at Tp and the onset of phasecoherence at the actual superconducting Tc. The ratio Tc/Tp decreases withgand vanishes atg =2. I present two complementary arguments of whythis happens. One is the softening of longitudinal gap fluctuations, whichbecome gapless at g =2. Another is the emergence ofa 1D array of dynamical vortices, whose number diverges at g =2. I arguethat a fundamentally novel superconducting ground state emerges at g>2.