Dynamics of superconducting pairs in the two-dimensional Hubbard model

Abstract

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 $\delta$ 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 $\delta$, 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.