Calculations of Spin Fluctuation Spectral Functions ${\alpha }^{2}F$ in High-Temperature Superconducting Cuprates

Abstract

Spin fluctuations have been proposed as a key mechanism for mediating superconductivity, particularly in high-temperature superconducting cuprates, where conventional electron-phonon interactions alone cannot account for the observed critical temperatures. Traditionally, their role has been analyzed through tight-binding based model Hamiltonians. In this work we present a method that combines density functional theory with a momentum- and frequency-dependent pairing interaction derived from the Fluctuation Exchange (FLEX) type Random Phase Approximation (FLEX-RPA) to compute Eliashberg spectral functions ${\alpha }^{2}F(\omega )$ which are central to spin fluctuation theory of superconductivity. We apply our numerical procedure to study a series of cuprates where our extracted material specific ${\alpha }^{2}F(\omega )$ are found to exhibit remarkable similarities characterized by a sharp peak in the vicinity of 40-60 meV and their rapid decay at higher frequencies. Our exact diagonalization of a linearized BCS gap equation extracts superconducting energy gap functions for realistic Fermi surfaces of the cuprates and predicts their symmetry to be $d_{x^2-y^2}$ in all studied systems. Via a variation of on-site Coulomb repulsion $U$ for the copper $d$-electrons we show that that the range of the experimental values of $T_c$ can be reproduced in this approach but is extremely sensitive to the proximity of the spin density wave instability. These data highlight challenges in building first-principle theories of high temperature superconductivity but offer new insights beyond previous treatments, such as the confirmation of the usability of approximate BCS-like $T_c$ equations, together with the evaluations of the material specific coupling constant $\lambda$ without reliance on tight-binding approximations of their electronic structures.

15 pages, 4 figures, 1 table

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