Metallic and superconducting fullerides, obtained by doping C60 crystals with alkalis, are a lattice of weakly coupled C60(3-) anions. The physics of the isolated ion is dominated by the orbital degeneracy of its electronic level and by the coupling with molecular vibrations, with a Jahn Teller (JT) effect leading to spin ½ ground state where two electrons out of three are paired.[1] Reasonably, therefore, the s-wave superconductivity of  metallic K3C60  and Rb3C60  had long been classified as BCS.[2] However, we had long suspected this picture as too simple, because for example the intra-fullerene Coulomb repulsion U  is larger that the electron bandwidth W.[3]  A striking confirmation came from Cs3C60 , recently shown to be a Mott insulator, turning metallic and superconducting only under pressure.[4] This and other results in fact strongly suggest that all fullerides are strongly correlated metals on the verge of a Mott transition, similar in that to the cuprates. To unravel this situation, which is unclear, we solved an orbitally degenerate Hubbard model, where <n>=3 electrons interact in each site via a Hubbard repulsion U, a Hund’s rule exchange JH, and an electron-vibron EJT. Large U favors a Mott insulating state, with either spin 3/2 if JH  were to prevail, or with spin ½ and pairing -- a  “Mott-Jahn-Teller” state [3] -- if EJT instead prevailed. Evidence that EJT prevails and Cs3C60 is  indeed a Mott-Jahn-Teller insulator is obtained by a first principles calculation of its IR spectrum, [5] and finding it in excellent agreement with recent measurements. [6]   Metallization of this special insulator finally yields a superconducting phase diagram with properties  in suggestive agreement with those of fullerides. [7] These materials provide in conclusion an instructive textbook case where strong correlations and electron-phonon coupling, rather than being alternative, actually cooperate and are both essential for superconductivity.
[1] A. Auerbach, N. Manini, E. Tosatti, PRB 49, 12998 (94); 49, 13008 (94)；[2] A.F. Hebard, M.J. Rosseinsky, R.C. Haddon, et al., Nature 350, 600 (91)；[3] M. Fabrizio, E. Tosatti, PRB 55, 13465 (97)；[4] A.Y. Ganin, Y. Takabayashi, Y.Z. Khimyak et al., Nat. Mat. 7, 367 (08);  Y.  Takabayashi, A. Y. Ganin, P. Jeglic, et al., Science 323, 1585 (09). [5] S.S. Naghavi, T. Qin, M. Fabrizio, E. Tosatti, to be published. [6] G. Klupp, P. Matus, K. Kamaras, et al.,  Nat. Commun. 3, 912 (12).[7] M. Capone, C. Castellani, M. Fabrizio, E. Tosatti, Rev. Mod. Phys. 81, 943 (09).