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Metal-insulator transition through a semi-Dirac point in oxide nanostructures: VO$_2$ (001) layers confined within TiO$_2$

Multilayer (TiO$_2$)$_m$/(VO$_2$)$_n$ nanostructures ($d^1$ - $d^0$ interfaces with no polar discontinuity) show a metal-insulator transition with respect to the VO$_2$ layer thickness in first principles calculations. For $n$ $\geq$ 5 layers, the system becomes metallic, while being insulating for $n$ = 1 and 2. The metal-insulator transition occurs through a semi-Dirac point phase for $n$ = 3 and 4, in which the Fermi surface is point-like and the electrons behave as massless along the zone diagonal in k-space and as massive fermions along the perpendicular direction. We provide an analysis of the evolution of the electronic structure through this unprecedented insulator-to-metal transition, and identify it as resulting from quantum confinement producing a non-intuitive orbital ordering on the V $d^1$ ions, rather than being a specific oxide interface effect. Spin-orbit coupling does not destroy the semi-Dirac point for the calculated ground state, where the spins are aligned along the rutile c-axis, but it does open a substantial gap if the spins lie in the basal plane.