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 (α2F)n(ω, θ) and (α2F)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 (α2F)n(ω, θ) for T just above Tc and below Tc. 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 (α2F)p,d(ω) required for the d-wave pairing instability at high temperatures as well as the deduced (α2F)n(θ, ω). We show that the deduced (α2F)n(θ, ω) can only be obtained from antiferromagnetic (AFM) fluctuations if their correlation length is smaller than a lattice constant. Using (α2F)p,d(ω) consistent with such a correlation length and the symmetry of matrix-elements scattering fermions by AFM fluctuations, we calculate Tc 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 (α2F)n(ω, θ). The pairing kernel (α2F)p,d(ω) calculated using the experimental values in the Eliashberg equation gives d-wave instability at Tc comparable to the experiments.