In the Eliashberg integral equations for d-wave superconductivity, two different functions $(alpha^2 F)_n(omega, theta)$ and $(alpha^2 F)_{p,d}(omega)$ 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$(alpha^2 F)_n(omega, theta)$. Besides its detailed $omega$ dependence, we find the remarkable result that this function is nearly independent of $theta$ between the ($pi,pi$)-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 $(alpha^2 F)_{p,d}(omega)$ required for the d-wave pairing instability at high temperatures as well as the deduced $(alpha^2 F)_n(theta, omega)$. We show that the deduced $(alpha^2 F)_n(theta, omega)$ can only be obtained from Antiferromagnetic (AFM) fluctuations if their correlation length is smaller than a lattice constant. Using $(alpha^2 F)_{p,d}(omega)$ 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 $theta$ and $omega$ dependence of the deduced $(alpha^2 F)_n(omega, theta)$. The pairing kernel $(alpha^2 F)_{p,d}(omega)$ calculated using the experimental values in the Eliashberg equation gives $d-wave$ instability at $T_c$ comparable to the experiments.
تحميل البحث