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-2 e 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. Fluctuations arising from proximity to an antiferromagnetic state may be a mechanism for electron pairing in high-temperature superconductors. Now numerics show that only about half of the pairing interaction can be attributed to spin fluctuations considered in spin fluctuation theory.