Retardation effects and the Coulomb pseudopotential in the theory of superconductivity

Abstract

In the theory of electron-phonon superconductivity both the magnitude of the electron-phonon coupling λ and the Coulomb pseudopotential μ* are important to determine the transition temperature Tc and other properties. We calculate corrections to the conventional result for the Coulomb pseudopotential. Our calculations are based on the Hubbard-Holstein model, where electron-electron and electron-phonon interactions are local. We develop a perturbation expansion, which accounts for the important renormalization effects for the electrons, the phonons, and the electron-phonon vertex. We show that retardation effects are still operative for higher order corrections, but less efficient due to a reduction of the effective bandwidth. This can lead to larger values of the pseudopotential and reduced values of Tc. The conclusions from the perturbative calculations are corroborated up to intermediate couplings by comparison with nonperturbative dynamical mean-field results.

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