Lecturer:  Andrey V Chubukov,   Universityof Minnesota, Minneapolis, USA    
Abstract:

I discussthe interplay between non-Fermi liquid behaviour and superconductivity near aquantum-critical point (QCP) in a metal. The tendencies towards superconductivity

and non-Fermi liquid behaviour compete:fermionic incoherence destroys the Cooper logarithm, while superconductivityeliminates scattering at low energies and restores fermionic coherence.  I argue the tendency towards pairing wins, butthe competition with non-Fermi liquid necessary leads to pseudogap behaviour inthe temperature range between the onset of the pairing at Tp and the actual superconductingTc.  I argue that there are two pseudogapregimes.  In some range below Tp thepairing is induced by fermions with the lowest Matsubara frequencies w_m =+- p T, for which fermionic self-energy is parametricallysmaller than at other w_m.  I arguethat in this regime superfluid stiffness is parametrically smaller than T, and superconductingorder is destroyed by long-wavelength phase fluctuations. At smaller T, butstill at T > Tc, superconducting coherence is lost due to phase slips,associated with the presence of a discrete, infinite set of solutions for thegap function at T=0.   I argue that there is a physically relevant model,in which this set becomes a continuous one, and long-range superconductingorder is destroyed already at T=0.  I discussthe behaviour of observables in the pseudogap regime and show that, e.g., the gapin the density of states fills in as T increases towards Tp, instead ofclosing.