Quantifying the role of antiferromagnetic fluctuations in the superconductivity of the doped Hubbard model

Superconductivity arises from the pairing of charge-e electrons into charge-2e bosons-called Cooper pairs-and their condensation into a coherent quantum state. The exact mechanism by which electrons pair up into Cooper pairs in high-temperature superconductors is still not understood. One of the plausible candidates is that spin fluctuations can provide an attractive effective interaction that enables this(1-3). Here we study the contribution of the electron-spin-fluctuation coupling to the superconducting state of the two-dimensional Hubbard model within dynamical cluster approximation(4) using a numerically exact continuous-time Monte Carlo solver(5). We show that only about half of the superconductivity can be attributed to a pairing mechanism arising from treating spin fluctuations as a pairing boson in the standard one-loop theory. The rest of the pairing interaction must come from as-yet unidentified higher-energy processes.