Mott switching and structural transition in the metal phase of $VO_2$ nanodomain.

$VO_2$ undergoes the insulator-metal transition (IMT) and monoclinic-rutile structural phase transition (SPT) near $67^oC$. The IMT switching has many applications. However, there is an unresolved issue whether the IMT is a Mott transition or a Peierls transition. This complication is caused by metal and insulator coexistence, which is an inherent property of the IMT region. Thus, the acquired data in the IMT region are averaged over the two phases in many experiments. We overcome the issue by probing the electronic state of the monoclinic structure and by introducing a model that accounts for the coexisting phases. We reveal the Mott IMT in the non-distorted monoclinic nanodomain between $55-63^oC$, and the distortion-assisted SPT above $60^oC$.