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We investigate the competition between the electron-vibron interaction(interaction with the Jahn-Teller phonons) and the Coulomb repulsion in asystem with local pairing of electrons on the triply degenerate lowestunoccupied molecular orbital (LUMO). The electron-vibron interaction radicallychanges conductivity and magnetic properties of alkali-doped fullerides AnC60,which should be antiferromagnetic Mott insulators: we have found that materialswith n=1,2 and A=K,Rb are conductors but not superconductors; n=3 and A=K,Rbare conductors (superconductors at low temperatures), but with A=Cs are Mottinsulators at normal pressure; n=2,4 are nonmagnetic Mott insulators. We haveshown that superconductivity, conductivity and insulation of these materialshave common nature. Based on the alkali-doped fullerides we propose ahypothetical material with a significantly higher critical temperature usingthe model of superconductivity with the external pair potential formulated in awork K.V. Grigorishin Phys. Lett. A 381 3089 (2017).

The role of electron-vibron interaction and local pairing in  conductivity and superconductivity of alkali-doped fullerides. The route to a  room-temperature superconductor