Consequences of extended-range interactions in the correlation-induced model of superconductivity in the fullerenes

A proposed model for superconductivity in the alkali-metal-doped fullerenes suggests that electrons pair together because of intramolecular correlation effects [S. Chakravarty and S. Kivelson, Europhys. Lett. 16, 751 (1991)]. With the use of perturbation theory, an effective attractive electron-electron interaction was found for a range of repulsive on-site Hubbard interaction U. We relax the on-site-only restriction by introducing a phenomenological model of statically screened Coulomb interactions and reexamine the original results. We present the consequences of extended interactions on the charged-fullerene ground states, the binding energies, the critical U necessary for pair binding, a nonphononic isotope effect, and the renormalization of the Coulomb pseudopotential parameter ${\mathrm{\mu }}^{\mathrm{*}}$. We find that Hund’s rule for a fullerene is violated depending on the strength and range of interaction. We determine the phase diagram for pair binding as a function of U (in units of the intrafullerene hopping t) and screening length for the electron filling appropriate for superconducting fullerenes. As the range of interaction increases towards physically reasonable estimates, the required U/t increases, delimiting the model as originally proposed. Our analysis of a nonphononic isotope effect also finds that U/t must be large and the interaction range short in order to describe observed shifts. In contrast, we find the proposed pair-binding model needs extended-range interactions to explain critical superconducting transition temperatures.