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We consider a quantum-critical metal with interaction mediated byfluctuations of a critical order parameter. This interaction gives rise to twocompeting tendencies -- pairing and non-Fermi liquid behavior. Due tocompetition, the pairing develops below a finite $T_p $, however its prominentfeedback on the fermionic self-energy develops only at a lower $ T_{cross}$. At$T<T_{cross}$ the system behavior is similar to that of a BCS supercoductor --the density of states (DOS) and the spectral function (SF) have sharp gapswhich close as $T$ increases. At higher $T_{cross}<T<T_{p}$ the DOS has a dip,which {\it fills in} with increasing $T$. The SF in this region shows eitherthe same behavior as the DOS, or has a peak at $\omega =0$ (the Fermi arc),depending on the position on the Fermi surface. We argue that phasefluctuations are strong in this $T$ range, and the actual $T_c \sim T_{cross}$,while $T_p$ marks the onset of pseugogap behavior. We compare our theory withthe behavior of optimally doped cuprates.

Superconductivity above a quantum critical point in a metal -- gap closing vs gap filling, Fermi arcs, and pseudogap behavior