Quantitative determination of pairing interactions for high-temperature superconductivity in cuprates

A profound problem in modern condensed matter physics is discovering and understanding the nature of fluctuations and their coupling to fermions in cuprates, which lead to high-temperature superconductivity and the invariably associated strange metal state. We report the quantitative determination of normal and pairing self-energies, made possible by laser-based angle-resolved photoemission measurements of unprecedented accuracy and stability. Through a precise inversion procedure, both the effective interactions in the attractive d-wave symmetry and the repulsive part in the full symmetry are determined. The latter is nearly angle-independent. Near T c, both interactions are nearly independent of frequency and have almost the same magnitude over the complete energy range of up to about 0.4 eV, except for a low-energy feature at around 50 meV that is present only in the repulsive part, which has less than 10% of the total spectral weight. Well below T c, they both change similarly, with superconductivity-induced features at low energies. Besides finding the pairing self-energy and the attractive interactions for the first time, these results expose the central paradox of the problem of high T c: how the same frequency-independent fluctuations can dominantly scatter at angles ±π/2 in the attractive channel to give d-wave pairing and lead to angle-independent repulsive scattering. The experimental results are compared with available theoretical calculations based on antiferromagnetic fluctuations, the Hubbard model, and quantum-critical fluctuations of the loop-current order.