Jahn-Teller distorsion and phase transitions in the alkali fullendes

In icosahedral symmetry, the LUMO of AnC60 molecule is a three-fold degenerate t1u orbital. For n equal 1 to 5, the partial filling of the band should confer a metallic behaviour and provide the possibility of a superconducting ground state. This is in disagreement with experimental data: only A3C60 seems to exhibit superconductivity and some examples of semiconducting compounds such as K4C60 or Rb4C60 prove the failure of this picture. This could be explained by a Jahn-Teller distorsion of the C60 molecule which leads to a partial lifting of the degeneracy of t1u orbital and could induce strong electronic correlations. In this model, tendency to localisation should prevail for even values of n, with completely filled subbands, but a superconductivity coupling is expected for odd values. The superconducting transition temperature should strongly decrease away from n = 3 on both sides of this maximum.