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 Tc. We show that near a QCP, fermions regain coherence only below a certain Tcross, which is smaller than the onset temperature for the pairing Tp. At T<Tcross 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 Tcross<T<Tp, 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 ω=0, depending on the position on the Fermi surface, leading to a Fermi arc. We argue that phase fluctuations are strong at T>Tcross, and the actual Tc≥Tcross, while at larger Tc<T<Tp 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≤Tc, and the persistence of the dip in the DOS and and the Fermi arc above Tc.
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Acknowledgment. We thank D. Dessau, A. Kanigel, A. Millis, N. Prokofiev, S. Raghu, M. Randeria, G. Torroba, and A. Yazdani for useful discussions. This work by Y.W. and A.V.C. was supported by the NSF DMR-1523036.
© 2019 American Physical Society.