Superconductivity in the A3C60 compounds is usually assumed to be driven by the electron-phonon interaction. Traditionally, superconductivity is analyzed in terms of the electron-phonon coupling lambda and the Coulomb pseudopotential mu*, where mu* describes the effects of the Coulomb repulsion on the superconductivity. For conventional superconductors mu* is argued to be small due to retardation effects, and the interest is focussed on the electron-phonon interaction. Since the retardation effects are expected to be inefficient at reducing mu* for the fullerenes, an important question has been if the large experimental Tc can be obtained within this frame work. A substantial part of the work has therefore aimed at estimating lambda and mu* to see if such estimates can give a Tc of the right order of magnitude. Since lambda and mu* might be of comparable magnitude, the estimate of mu* is as important as the estimate of lambda. We find that mu* should be substantially reduced by screening effects.

Due to the importance of mu*, it is somewhat artificial to treat the electron-phonon and the electron-electron interaction separately. The two interactions can be treated on an equal footing in the dynamical mean-field theory (DMFT). The treatment of conventional superconductors is usually based on the Migdal-Eliashberg theory, assuming the phonon frequencies are much smaller than the band width. This assumption is not satisfied for the fullerenes, and it is naturally avoided in the DMFT theory. Using a DMFT treatment, we find that a local pairing on the C60 molecules plays a very important role, meaning that the Coulomb repulsion is much less damaging to superconductivity than one might have thought. This approach can also explain the strong doping dependence seen experimentally. Putting U=0, we finally find that the Migdal-Eliashberg theory is surprisingly good.

We find that the superconductivity in the alkali-doped fullerenes essentially differs from the picture of conventional superconductors, in the sense that the Coulomb repulsion is mainly overcome by local pairing and screening effects instead of retardation effects. The molecular solid character of C60 and the presence of Jahn-Teller phonons are essential for these results.