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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” self-energy and the “pairing” self-energy. ω is the frequency of fluctuations scattering the fermions whose momentum is near the Fermi-surface and makes an angle θ to a chosen axis. We present a quantitative analysis of the high-resolution laser based Angle Resolved Photoemission Spectroscopy (ARPES) data on a slightly under doped cuprate compound Bi2212 and use the Eliashberg equations to deduce the ω and θ dependence of (α 2 F) n (ω, θ) for T just above T c and below T c. 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, except for the dependence of the cut-off energy on θ. 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 by AFM fluctuations, we calculate T c and show that AFM fluctuations are excluded as the pairing mechanism for d-wave superconductivity in cuprates. We also consider the quantumcritical fluctuations derived microscopically as the fluctuations of the observed loop-current order discovered in the under-doped cuprates, and which lead to the marginal Fermi-liquid properties in the normal state. 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.

Superconductivity in the cuprates: Deduction of mechanism for d-wave pairing through analysis of ARPES