On the possible significance of electronic correlations for phonon-induced superconductivity

Abstract

We adapt an interpolation formula for the superconducting transition temperature T c derived from the Eliashberg equations to the two-site Hubbard model accomplished by electron-phonon interaction. An exact treatment of electronic correlations shows a general tendency towards an enhancement of T c by on-site Coulomb repulsion. This feature is partially reproduced in an approximate treatment of the problem (saddle point approximation for auxiliary boson fields). The latter result suggests looking for this effect in the realistic, finite band width version of the Hubbard model.