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