Metal-Insulator Transition in ${\mathrm{VO}}_2$: A $\mathrm{DFT}+\mathrm{DMFT}$ Perspective

We present a theoretical investigation of the electronic structure of rutile (metallic) and $M_1$ and $M_2$ monoclinic (insulating) phases of ${\mathrm{VO}}_2$ employing a fully self-consistent combination of density functional theory and embedded dynamical mean field theory calculations. We describe the electronic structure of the metallic and both insulating phases of ${\mathrm{VO}}_2$, and propose a distinct mechanism for the gap opening. We show that Mott physics plays an essential role in all phases of ${\mathrm{VO}}_2$: undimerized vanadium atoms undergo classical Mott transition through local moment formation (in the $M_2$ phase), while strong superexchange within V dimers adds significant dynamic intersite correlations, which remove the singularity of self-energy for dimerized V atoms. The resulting transition from rutile to dimerized $M_1$ phase is adiabatically connected to the Peierls-like transition, but is better characterized as the Mott transition in the presence of strong intersite exchange. As a consequence of Mott physics, the gap in the dimerized $M_1$ phase is temperature dependent. The sole increase of electronic temperature collapses the gap, reminiscent of recent experiments.

Figure 1

$\mathrm{DFT}+\mathrm{DMFT}$-based total (black dashed line) and projected DOS of (a) $R$ and (b) $M_1$ phase of ${\mathrm{VO}}_2$. The projections to $a_{1g}$, $e_g^{\pi }(1)$, $e_g^{\pi }(2)$, and $e_g^{\sigma }$ states are shown in blue, red, green, and brown lines, respectively. For the $M_1$ phase, the solid (dashed) blue line corresponds to the projection on the bonding (antibonding) $a_{1g}$ molecular state.

Figure 2

(a) Real part of the optical conductivity of $R$, $M_1$, and $M_2$ phases of ${\mathrm{VO}}_2$. (b) Real part of intersite self-energies, on an imaginary frequency axis, of $a_{1g}\text{−}{a}_{1g}$ (black) and $e_g^{\pi }(1)\text{−}{e}_g^{\pi }(1)$ (red) states of $M_1$ phase. (c) Imaginary part, on real frequency axis, of bonding (dashed lines) and antibonding (solid lines) self-energies associated with the $a_{1g}$ (orange) and $e_g^{\pi }(1)$ (cyan) dimer electronic states.

Figure 3

Spectral function and projected DOS of $M_1$ phase at 332 (a) and 900 K (b). In (c) the spectral function of $M_2$ phase at 332 K is shown.

Figure 4

(a) $\mathrm{Re}{\mathrm{\Sigma }}_{a_{1g}-a_{1g}}^{\mathrm{in}}(i\omega )$ at 332 K (dashed lines) and 900 K (solid lines) of $M_1$ phase. Inset: $\mathrm{Re}{\mathrm{\Sigma }}_{ab,a_{1g}}(\omega )$ (blue) and $\mathrm{Re}{\mathrm{\Sigma }}_{b,e_g^{\pi }(1)}(\omega )$ (red) at 332 (dashed lines) and 900 K (solid lines). (b) $\mathrm{Re}{\mathrm{\Sigma }}_{a_{1g}}(\omega )$ of undimerized V atoms in the antiferromagnetic phase of $M_2$ phase. (c) $\mathrm{Im}\mathrm{\Sigma }(\omega )$ of bonding and antibonding $a_{1g}$ self-energies of V dimers (orange lines) and $a_{1g}$ states of undimerized V atoms (black lines).