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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 tcs, 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.
We present a first-principles approach to describe magnetic and superconducting systems and the phenomena of competition between these electronic effects. We develop a density functional theory: SpinSCDFT, by extending the Hohenberg-Kohn theorem and
We address an issue of how to accurately include the self energy effect of the screened electron-electron Coulomb interaction in the phonon-mediated superconductors from first principles. In the Eliashberg theory for superconductors, self energy is u
The newly discovered iron pnictide superconductors apparently present an unusual case of interband-channel pairing superconductivity. Here we show that, in the limit where the pairing occurs within the interband channel, several surprising effects oc
The standard Eliashberg - McMillan theory of superconductivity is essentially based on the adiabatic approximation. Here we present some simple estimates of electron - phonon interaction within Eliashberg - McMillan approach in non - adiabatic and ev
We numerically investigate the Spin Density Functional theory for superconductors (SpinSCDFT) and the approximated exchange-correlation functional, derived and presented in the preceding paper I. As a test system we employ a free electron gas featuri