Dynamics of superconducting pairs in the two-dimensional Hubbard model

TL;DR

This study uses cellular dynamical mean-field theory to analyze the frequency-dependent superconducting correlations in the two-dimensional Hubbard model, revealing that pairing is driven by superexchange interactions rather than on-site Coulomb repulsion.

Contribution

It provides a systematic quantification of how doping and interaction strength affect the frequency scales and mechanisms of $d$-wave pairing in the Hubbard model.

Findings

Pair-forming processes are confined to frequencies set by superexchange interaction.

Pair-breaking processes occur at different frequency scales, not on the scale of U.

High-frequency effects of U are eliminated by d-wave pairing, emphasizing superexchange-driven pairing.

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.