Superconductivity of Rb 3 C 60 : 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 α ² F (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 α ² F (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. Received 30 March 2001