SUPERCONDUCTIVITY MECHANISMS IN DOPED C60

The high-T(c) superconductivity in C60 compounds is studied in relation to the graphite intercalation compounds that show instead a very low T(c). The electron-phonon coupling-lambda is slightly higher for the C60 compounds but the main difference comes from the fact that in C60 the Fermi energy is comparable to the phonon frequency. This leads to a breakdown of Migdal's theorem and to the corresponding vertex renormalization. These new many-body effects lead to a strong enhancement of T(c) with respect to the BCS theory in contrast to the usual Eliashberg-McMillan theory that gives instead a reduction. This can explain the properties of the C60 and the graphite compounds, it reopens the question of the maximum T(c) and it should have implications also with respect to the cuprate high-T(c) superconductors.