Nonadiabatic superconductivity in fullerene-based materials

Fullerene compounds have phonon frequencies up to ω_max=0.2 eV and a Fermi energy of the order E_F=0.3 eV. It is, therefore, expected that the adiabatic parameter λω_ph/E_F (where λ is the electron-phonon coupling constant and ω_ph is a typical phonon frequency) is not a priori negligible and the conventional theory of phonon-mediated superconductivity is inapplicable in this case. Here, we discuss how the conventional theory is inconsistent with a number of experimental data and provide a generalization of the theory in order to include nonadiabatic electron-phonon effects. We show that the inclusion of nonadiabatic channels in the electron-phonon interaction is a key element for the high values of T_c in these materials. We make several predictions regarding the superconducting and normal-state properties of fullerene compounds that can be tested experimentally.