<i>Ab initio</i> theory of plasmonic superconductivity within the Eliashberg and density-functional formalisms
Arkadiy Davydov, Antonio Sanna, Camilla Pellegrini, J. K. Dewhurst, S. Sharma, E. K. U. Gross
Abstract
We extend the two leading methods for the ab initio computational description of phonon-mediated superconductors, namely Eliashberg theory and density-functional theory for superconductors (SCDFT), to include plasmonic effects. Furthermore, we introduce a hybrid formalism in which the Eliashberg approximation for the electron-phonon coupling is combined with the SCDFT treatment of the dynamically screened Coulomb interaction. The methods have been tested on a set of well-known conventional superconductors by studying how the plasmon contribution affects the phononic mechanism in determining the critical temperature $({T}_{C})$. Our simulations show that plasmonic SCDFT leads to a good agreement between predicted and measured ${T}_{C}$'s, whereas Eliashberg theory considerably overestimates the plasmon-mediated pairing and, therefore, ${T}_{C}$. The hybrid approach, on the other hand, gives results close to SCDFT and overall in excellent agreement with experiments.