1212.2975 (Johannes Bauer et al.)

Retardation effects and the Coulomb pseudopotential in the theory of
superconductivity    [PDF]

Johannes Bauer, Jong E. Han, Olle Gunnarsson

In the theory of electron-phonon superconductivity both the magnitude of the electron-phonon coupling $\lambda$ as well as the Coulomb pseudopotential $\mu^*$ are important to determine the transition temperature $T_c$ and other properties. We calculate corrections to the conventional result for the Coulomb pseudopotential. Our calculation 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 $T_c$. The conclusions from the perturbative calculations are corroborated up to intermediate couplings by comparison with non-perturbative dynamical mean-field results.

View original: http://arxiv.org/abs/1212.2975