Eliashberg equations and the phenomenology of field-effect-doped C60

In a recent paper [J. H. Schön, Ch. Kloc, R. C. Haddon and B. Batlogg, Nature 408, 549 (2000)] C60 doped with holes by application of an intense electric field was found to superconduct at remarkably high temperature. In this paper we show that the observed dependence of Tc on doping can be reproduced by solving the (four) s-wave Eliashberg equations in the case of a finite, non-half-filled energy band, with the only initial hypothesis that the Coulomb pseudopotential depends on the filling in a very simple and plausible way. The experimental data are reproduced by using very reasonable values of the physical parameters involved. We also show that the application of the same approach to new experimental data [ J. H. Schön, Ch. Kloc and B. Batlogg, Science 293, 2432 (2001)] also gives good results.