Possible explanation of electric-field-doped C60 phenomenology in the framework of Eliashberg theory

In a recent paper [J. H. Schön, Ch. Kloc, R. C. Haddon, and B. Batlogg, Nature (London) 408, 549 (2000)] a large increase in the superconducting critical temperature was observed in C60 doped with holes by application of a high electric field. We demonstrate that the measured Tc versus doping curves can be explained by solving the (four) s-wave Eliashberg equations in the case of a finite, non-half-filled energy band. In order to reproduce the experimental data, we assume a Coulomb pseudopotential depending on the filling in a very simple and plausible way. Reasonable values of the physical parameters involved are obtained. The application of the same approach to other experimental data [J. H. Schön, Ch. Kloc, and B. Batlogg, Science 293, 2432 (2001)] on electric field-doped, lattice-expanded C60 single crystals (Tc = 117 K in the hole-doped case) gives equally good results and sets a theoretical limit to the linear increase of Tc at the increase of the lattice spacing.