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Superconductivity in the Cuprates: Deduction of Mechanism for D-Wave Pairing Through Analysis of ARPES

In the Eliashberg integral equations for d-wave superconductivity, two different functions $(α^2 F)_n(ω, θ)$ and $(α^2 F)_{p,d}(ω)$ determine, respectively, the "normal" and the "pairing" self-energies. We present a quantitative analysis of the high-resolution laser based ARPES data on the compound Bi-2212 to deduce the function$(α^2 F)_n(ω, θ)$. Besides its detailed $ω$ dependence, we find the remarkable result that this function is nearly independent of $θ$ between the ($π,π$)-direction and 25 degrees from it. Assuming that the same fluctuations determine both the normal and the pairing self-energy, we ask what theories give the function $(α^2 F)_{p,d}(ω)$ required for the d-wave pairing instability at high temperatures as well as the deduced $(α^2 F)_n(θ, ω)$. We show that the deduced $(α^2 F)_n(θ, ω)$ can only be obtained from Antiferromagnetic (AFM) fluctuations if their correlation length is smaller than a lattice constant. Using $(α^2 F)_{p,d}(ω)$ consistent with such a correlation length and the symmetry of matrix-elements scattering fermions off AFM fluctuations, we calculate $T_c$ an show that AFM fluctuations are excluded as the pairing mechanism for d-wave superconductivity in cuprates. We also consider the quantum-critical fluctuations derived microscopically as the fluctuations of the observed loop-current order discovered in the under-doped cuprates. We show that their frequency dependence and the momentum dependence of their matrix-elements to scatter fermions are consistent with the $θ$ and $ω$ dependence of the deduced $(α^2 F)_n(ω, θ)$. The pairing kernel $(α^2 F)_{p,d}(ω)$ calculated using the experimental values in the Eliashberg equation gives $d-wave$ instability at $T_c$ comparable to the experiments.