## **The metal-insulator transition of VO**_{2}

### Institut für Physik, Universität Augsburg

Despite intense work over four decades the metal-insulator transition of
VO_{2} is still far from being understood. To some part this is
due to the simultaneous occurance of a structural transformation, which
fact hindered to clearly identify the structural or the electronic degrees
of freedom as the origin of the transition. Several models have been
proposed ranging from Peierls-, spin-Peierls- to Mott-Hubbard-type scenarios,
which stress, to a different degree, the role of lattice instabilities,
electron-phonon interaction and electronic correlations. Yet, neither of
these pictures has so far been successful in explaining a broader range of
the physical phenomena showing up in VO_{2}.

We present results of electronic structure calculations for VO_{2}
as based on density functional theory. As a calculational scheme we used
the augmented spherical wave (ASW) method. Both the high-temperature
rutile phase and the low-temperature monoclinic M_{1} phase were
considered. They differ mainly by two fundamental displacements occuring
in the characteristic vanadium chains, namely, a V-V dimerization and a
zigzag-like antiferroelectric V shift. For the rutile phase we find V
*3d t*_{2g} states near the Fermi energy, which have small
admixtures from O *2p* states due to π-type bonding. These
vanadium bands fall into two groups: While the almost perfect one-dimensional
dispersion of the V *3d*_{x2-y2} states
reflects the metal-metal overlap along the chains the remaining
*t*_{2g} bands display a more three-dimensional dispersion.
On going from the rutile to the monoclinic stucture, the
V *3d*_{x2-y2} states show a strong
bonding-antibonding splitting due to the dimerization. In contrast, the
other two bands shift to higher energies as a consequence of the
antiferroelectric mode. The result is an effective energetic separation
of both groups, which, however, still show a tiny semimetallic-like band
overlap due to the shortcomings of the local density approximation.

We performed additional calculations for the insulating monoclinic
M_{2} phase of VO_{2}, where only half of the chains
dimerize. The antiferroelectric shifts are limited to the remaining chains,
which, in addition, display antiferromagnetic order. While we obtain for
the dimerizing chains a similar picture as for the M_{1} phase,
lifting the spin degeneracy leads to splitting of the
V *3d*_{x2-y2} states on the zigzag
chains. As a consequence, these states are again separated from the other
*t*_{2g} bands with the tiny band overlap still remaining.
To conclude, though the helping hand of electronic correlations seems to
be needed for a complete gap opening, the metal-insulator transition of
VO_{2} arises predominantly from structural and magnetic
instabilities of the rutile phase.

*Last change: 1999-10-26*

*© 1999-1999 Volker Eyert*