Eliashberg theory for spin fluctuation mediated superconductivity: Application to bulk and monolayer FeSe

Abstract

We present a novel method for embedding spin and charge fluctuations in an anisotropic, multiband, and full-bandwidth Eliashberg treatment of superconductivity. Our analytical framework, based on the random phase approximation, allows for a self-consistent calculation of material-specific characteristics in the interacting, and more specifically, the superconducting state. We apply this approach to bulk FeSe as a representative for the iron-based superconductors and successfully solve for the superconducting transition temperature Tc, the gap symmetry, and the gap magnitude. We obtain Tc≈6 K, consistent with experiment (Tc≈8 K), as well as other quantities in good agreement with experimental observations, thus supporting spin fluctuations mediated pairing in bulk FeSe. On the contrary, applying our approach to monolayer FeSe on SrTiO3 we find that spin fluctuations within the full Eliashberg framework give a d-wave gap with Tc≤11 K and therefore cannot provide an explanation for a critical temperature as high as observed experimentally (Tc≈70 K). Our results hence point towards interfacial electron-phonon coupling as the dominant Cooper pairing mediator in this system.