We consider a metal with interaction mediated by fluctuations of an order parameter, which condenses at a quantum critical point (QCP). This interaction gives rise to fermionic incoherence in the normal state and also mediates pairing. Away from a QCP, the pairing restores fermionic coherence almost immediately below $T_c$. We show that near a QCP, fermions regain coherence only below a certain $T_{\text{cross}}$, which is smaller than the onset temperature for the pairing $T_p$. At $T<T_{\text{cross}}$ the system behavior is conventional in the sense that both the density of states (DOS) and the spectral function (SF) have sharp gaps, which close in as $T$ increases. At higher $T_{\text{cross}}<T<T_p$, the DOS has a dip, which fills in with increasing $T$, while the SF shows either the same behavior as the DOS, or has a peak at $\omega =0$, depending on the position on the Fermi surface, leading to a Fermi arc. We argue that phase fluctuations are strong at $T>T_{\text{cross}}$, and the actual $T_c\ge T_{\text{cross}}$, while at larger $T_c<T<T_p$ the system displays a pseudogap behavior. We argue that our theory explains the crossover from gap closing to gap filling, observed in cuprate superconductors at $T\le T_c$, and the persistence of the dip in the DOS and and the Fermi arc above $T_c$.

• Received 18 December 2018

DOI:https://doi.org/10.1103/PhysRevB.99.180506