Eliashberg theory in the uniform electron gas revisited

The Eliashberg theory with the Migdal approximation has been established as a standard ab initio theory for phonon-mediated superconductor. But accurate treatment of electron-electron Coulomb interaction effects there has remained under debate. Historically the electronic interaction in nearly uniform superconductors has been of interest in the context of the plasmon superconductivity, whereas the recent interest is on a more quantitative aspect: to which extent it finally suppress or enhance Tc on top of the phonon-mediated pairing attraction. The latter is wholly a quantitative problem but has become important with the recent invention of high-temperature hydride superconductors, where the treatment of the pairing interactions affects the estimated Tc by several ten Kelvin.

In this presentation we review and explore the plasmonic effects that compete for Tc; plasmon-mediated pairing and plasmon self energy effects. The latter in realistic systems has not been investigated thoroughly because of computational cost required. We study the effects in the uniform electron gas (UEG) with a modeled electron-phonon interaction, whose properties should broadly apply to various conventional superconductors. We attempt to relate classic studies on UEG to the current studies on the effective Morel-Anderson pseudopotential, to build a basis for the first-principles and semiempirical Eliashberg calculations for conventional superconductors.