Dynamics of Superconducting Pairs in the Two-Dimensional Hubbard Model

The frequency structure of the superconducting correlations in cuprates gives insights on the pairing mechanism. Here we present an exhaustive study of this problem in the two-dimensional Hubbard model with cellular dynamical mean-field theory. To this end, we systematically quantify the dependence on doping 𝛿 and interaction strength 𝑈 of the superconducting gap, of the frequency scales where 𝑑-wave pairing occurs, and of their relative contribution to pairing. For all values of 𝑈 and 𝛿, we find pair-forming processes confined to frequencies set by the superexchange interaction and followed by pair-breaking processes, ruling out both pair-forming and pair-breaking processes on the scale of 𝑈. This suggests that at high frequencies, the effect of 𝑈 is eliminated by the 𝑑-wave paring, and that at small frequencies, 𝑈 generates the superexchange interaction that leads to low-frequency pair-forming processes providing the net contribution to pairing.