The Coulomb interaction U between two electrons on the same molecule and the width W of the populated t1u band are important parameters for the AnC60 compounds. The ratio U/W is substantially larger (1.5-2.5) than unity for A3C60, and one would therefore expect the system to be a Mott-Hubbard insulator according to traditional theory.
A simple argument shows, however, that the orbital degeneracy should tend to increase the critical value Uc where the transition takes place ( Phys. Rev. B 54, R11026 (1996)). This argument is supported by exact diagonalization and T=0 lattice Quantum Monte Carlo calculations. The increase of the critical value of U/W is due to an increased importance of hopping in systems with a large orbital degeneracy. This has been studied further in the limit of a large U (Phys. Rev. B 56 , 1146 (1997)). The critical value of U/W also depends on the (integer) filling of the band (Phys. Rev. B 60, 15714 (1999)).
An interesting question is why the A3C60 compounds are metals but the A4C60 compounds are insulators, although the U/W is only slightly larger for A4C60. An important factor ( Phys. Rev. Lett. 84, 1276 (2000) ) is the different lattice structures, fcc (A3C60) and bct (A4C60). In the fcc lattice it is possible to hop along a closed path (e.g., a triangle) in an odd number of hops, while this is not possible for the bct lattice if only nearest neighbor hopping is considered. This frustration of the fcc lattice leads to a substantially smaller one-particle band width W for a given hopping strength than for the (almost) unfrustrated bct lattice. The frustration only shows up in a much reduced form in the many-body calculation. The suppressed value of W then leads to an increased ratio of U/W for the metal-insulator transition for the fcc lattice.
A model with just a Hubbard U predicts A4C60 to be an antiferromagnet, in contrast to the experimental observation of a nonmagnetic state. A proper description therefore requires the inclusion of the electron-phonon coupling and the competition between the Jahn-Teller effect (favoring a low-spin state) and the Hund's rule coupling (favoring a high-spin state). Estimates of the parameters suggest that the low-spin states wins, in agreement with experiment. In addition we find that ( Phys. Rev. Lett. 84, 1276 (2000), Physica B 292, 196 (2000) )
1. Coupling to Hg reduces Uc/W, while the coupling to Ag increases Uc/W.
2. The competition between the Jahn-Teller effect and the Hund's rule coupling reduces the effect of the Hg on Uc/W.