The role of electron-vibron interaction and local pairing in conductivity and superconductivity of alkali-doped fullerides

We investigate the competition between the electron-vibron interaction (interaction with the Jahn-Teller phonons) and the Coulomb repulsion in a system with the local pairing of electrons on the 3-fold degenerate lowest unoccupied molecular orbital (LUMO). The el.-vib. interaction and the local pairing radically change conductivity and magnetic properties of alkali-doped fullerides $\texttt{A}_{n}\texttt{C}_{60}$, which would have to be antiferromagnetic Mott insulators: we have shown that materials with $n=1,5$ and $\texttt{A}=\texttt{K},\texttt{Rb}$ are conductors but not superconductors; $n=3$ and $\texttt{A}=\texttt{K},\texttt{Rb}$ are conductors and superconductors at low temperatures, but with $\texttt{A}=\texttt{Cs}$ they are Mott-Jahn-Teller insulators at normal pressure; $n=2,4$ are nonmagnetic Mott insulators. Thus superconductivity, conductivity and insulation of these materials have common nature. Using this approach we obtain the phase diagram of $\texttt{A}_{3}\texttt{C}_{60}$ analytically, which is the result of interplay between the local pairing, the el.-vib. interaction, Coulomb correlations, and formation of small radius polarons.