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The normal state of strongly coupled superconductors is characterized by thepresence of "preformed" Cooper pairs well above the superconducting criticaltemperature. In this regime, the electrons are paired, but they lack the phasecoherence necessary for superconductivity. The existence of preformed pairsimplies the existence of a characteristic energy scale associated to apseudogap. Preformed pairs are often invoked to interpret systems where somesignatures of pairing are present without actual superconductivity, but anunambiguous theoretical characterization of a preformed-pair system is stilllacking. To fill this gap, we consider the response to an external pairingfield of an attractive Hubbard model, which hosts one of the cleanestrealizations of a preformed pair phase, and a repulsive model where s-wavesuperconductivity can not be realized. Using dynamical mean-field theory tostudy this response, we identify the characteristic features which distinguishthe reaction of a preformed pair state from a normal metal without anyprecursor of pairing. The theoretical detection of preformed pairs isassociated with the behavior of the second derivative of the order parameterwith respect to the external field, as confirmed by analytic calculations inlimiting cases. Our findings provide a solid testbed for the interpretation ofstate-of-the-art calculations for the normal state of the doped Hubbard modelin terms of d-wave preformed pairs and, in perspective, of non-equilibriumexperiments in high-temperature superconductors.

Detecting a preformed pair phase: The response to a pairing forcing field