On the metal-insulator-transition in vanadium dioxide

Vanadium dioxide (VO$_2$) undergoes a metal-insulator transition (MIT) at 340 K with the structural change from tetragonal to monoclinic crystal. The conductivity $\sigma$ drops at MIT by four orders of magnitude. The low temperature monoclinic phase is known to have a lower ground-state energy. The existence of the $k$-vector ${\mathbf k}$ is prerequisite for the conduction since the ${\mathbf k}$ appears in the semiclassical equation of motion for the conduction electron (wave packet). The tetragonal (VO$_2)_3$ unit is periodic along the crystal's $x$-, $y$-, and $z$-axes, and hence there is a three-dimensional $k$-vector. There is a one-dimensional ${\mathbf k}$ for a monoclinic crystal. We believe this difference in the dimensionality of the $k$-vector is the cause of the conductivity drop.