Andersen Group | El.-Phon. | QMC | C60 | GW | Resistivity saturation |
Metal-insulator transition |
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.
Andersen Group |
Max-Planck-Institut für Festkörperforschung Heisenbergstraße 1 D-70569 Stuttgart |