Ab initio theory of plasmonic superconductivity within the Eliashberg and density-functional formalisms

TL;DR

This paper develops and tests advanced ab initio methods incorporating plasmonic effects into superconductivity calculations, demonstrating improved accuracy in predicting critical temperatures compared to traditional approaches.

Contribution

It introduces a hybrid formalism combining Eliashberg theory and SCDFT to accurately account for plasmonic effects in superconductors.

Findings

SCDFT with plasmons matches experimental Tc well

Eliashberg overestimates plasmonic pairing effects

Hybrid method aligns closely with experimental results

Abstract

We extend the two leading methods for the \emph{ab initio} computational descrip tion of phonon-mediated superconductors, namely Eliashberg theory and density fu nctional theory for superconductors (SCDFT), to include plasmonic effects. Furth ermore, we introduce a hybrid formalism in which the Eliashberg approximation fo r the electron-phonon coupling is combined with the SCDFT treatment of the dynam ically screened Coulomb interaction. The methods have been tested on a set of we ll-known conventional superconductors by studying how the plasmon contribution a ffects the phononic mechanism in determining the critical temperature (\tc). Our simulations show that plasmonic SCDFT leads to a good agreement between predict ed and measured \tc's, whereas Eliashberg theory considerably overestimates the plasmon-mediated pairing and, therefore, \tc. The hybrid approach, on the other hand, gives results close to SCDFT and overall in excellent agreement with exper iments.