Non adiabatic superconductivity of a correlated Fermi liquid: Application to fullerides

We describe superconducting Fullerides by a model of weakly coupled molecular levels, in which the bandwidth B and the Debye energy ωD have same orders of magnitude. For such a narrow band, electron correlations are supposed to be important. They are discussed in a Hubbard model, using a Gutzwiller approach, which modifies the electron propagators. The gap equation for superconductivity is written in the Eliashberg strong coupling theory. Assuming a simple Fröhlich electron-electron attraction, induced by the electron-phonon coupling, the critical temperature of superconductivity is calculated as a function of B/U, where U is the Hubbard Coulomb energy. Effects of non adiabaticity associated to large Debye energy is discussed by including correlations to Migdalʹs theorem. A connection between the critical temperature and the screening effect is made.