Superconductivity of Rb3C60: breakdown of the Migdal-Eliashberg theory

In this paper, through an exhaustive analysis within the Migdal-Eliashberg theory, we show the incompatibility of experimental data of Rb3C60 with the basic assumptions of the standard theory of superconductivity. For different models of the electron-phonon spectral function α2F(Ω) we solve numerically the Eliashberg equations to find which values of the electron-phonon coupling λ, of the logarithmic phonon frequency and of the Coulomb pseudopotential μ* reproduce the experimental data of Rb3C60. We find that the solutions are essentially independent of the particular shape of α2F(Ω) and that, to explain the experimental data of Rb3C60, one has to resort to extremely large couplings: λ = 3.0±0.8. This results differs from the usual partial analyses reported up to now and we claim that this value exceeds the maximum allowed λ compatible with the crystal lattice stability. Moreover, we show quantitatively that the obtained values of λ and strongly violate Migdal's theorem and consequently are incompatible with the Migdal-Eliashberg theory. One has therefore to consider the generalization of the theory of superconductivity in the nonadiabatic regime to account for the experimental properties of fullerides.