Orbital-selective insulator-metal transition in ${\mathrm{V}}_2{\mathrm{O}}_3$ under external pressure

We present a detailed account of the physics of vanadium sesquioxide $\left({\mathrm{V}}_2{\mathrm{O}}_3\right)$, a benchmark system for studying correlation-induced metal-insulator transition(s). Based on a detailed perusal of a wide range of experimental data, we stress the importance of multiorbital Coulomb interactions in concert with first-principles local-density approximation (LDA) band structure for a consistent understanding of the insulator-metal (IM) transition under pressure. Using $\mathrm{LDA}+\mathrm{DMFT}$ (dynamical mean-field theory), we show how the IM transition is of the orbital selective type, driven by large changes in dynamical spectral weight in response to small changes in trigonal field splitting under pressure. Very good quantitative agreement with (i) the switch of orbital occupation and (ii) $S=1$ at each $V^{3+}$ site across the IM transition, and (iii) carrier effective mass in the paramagnetic phase, is obtained. Finally, using the $\mathrm{LDA}+\mathrm{DMFT}$ solution, we have estimated screening-induced renormalization of the local, multiorbital Coulomb interactions. Computation of the one-particle spectral function using these screened values is shown to be in excellent quantitative agreement with very recent experimental (photoemission and x-ray-absorption spectroscopy) results. These findings provide strong support for an orbital-selective Mott transition in paramagnetic ${\mathrm{V}}_2{\mathrm{O}}_3$.

Figure 1

(Color online) Three-dimensional view of the corundum lattice structure of ${\mathrm{V}}_2{\mathrm{O}}_3$. The crystallographic $(z,x)$ axes are depicted on the lower right side in the figure.

Figure 2

Phase diagram of ${\mathrm{V}}_{2-x}{\mathrm{M}}_x{\mathrm{O}}_3$ with $\mathrm{M}=\mathrm{Cr},\mathrm{Ti}$, showing the AFI, PI, and PM phases as a function of chemical pressure $\left(x\right)$ in the temperature “pressure” plane; data points are taken from Ref. 7.

Figure 3

(Color online) Crystal structure of ${\mathrm{V}}_2{\mathrm{O}}_3$ in the low-temperature, antiferromagnetically ordered, monoclinic phase. The arrows indicate the orientations of the spins on each Vanadium site. The crystallographic $(z,x)$ axes are depicted on the lower right side in the figure.

Figure 4

(Color online) LDA partial density of states for the $e_g^{\pi }$ (dashed red line) and $a_{1g}$ (solid blue line) orbitals, obtained from Ref. 30.

Figure 5

(Color online) Orbital-resolved (upper panels) and total (lower panel) one electron spectral function for the insulating phase of ${\mathrm{V}}_2{\mathrm{O}}_3$ obtained with $5.0\mathrm{eV}$ and $J_H=1.0\mathrm{eV}$.

Figure 6

(Color online) Orbital-resolved (upper panels) and total (lower panel) one-electron spectral functions for the metallic phase of ${\mathrm{V}}_2{\mathrm{O}}_3$. Note that only the $a_{1g}$-orbital DOS crosses $E_F$ in the metallic phase; the $e_g^{\pi }$ orbitals still shows Mott-Hubbard insulating features, showing the “two-fluid” character of the MIT in ${\mathrm{V}}_2{\mathrm{O}}_3$.

Figure 7

(Color online) Effect of temperature $T$ on the orbital-resolved (upper panel) and total (lower panel) one electron spectral functions for the insulating phase of ${\mathrm{V}}_2{\mathrm{O}}_3$.

Figure 8

(Color online) Effect of temperature $T$ on the orbital-resolved (upper panels) and total (lower panel) one electron spectral functions for the metallic phase of ${\mathrm{V}}_2{\mathrm{O}}_3$.

Figure 9

(Color online) Effect of disorder $\left(\nu \right)$ with a binary-alloy distribution on the orbital-resolved (upper panels) and total (lower panel) one-electron spectral functions for the metallic phase of ${\mathrm{V}}_2{\mathrm{O}}_3$.

Figure 10

(Color online) Comparison of theoretical $\mathrm{LDA}+\mathrm{DMFT}$ result (solid blue line) for the total one-electron spectral function in the metallic phase of ${\mathrm{V}}_2{\mathrm{O}}_3$ to the experimental results taken from Refs. 14, 15 (for PES) and from Ref. 43 (for XAS).

Figure 11

(Color online) Comparison of two different $\mathrm{LDA}+DMFT$ results for the total one-electron spectral function in the metallic phase of ${\mathrm{V}}_2{\mathrm{O}}_3$ to the experimental results of PES taken from Refs. 14, 15. The $\mathrm{LDA}+\mathrm{DMFT}\left(\mathrm{QMC}\right)$ result is taken from Ref. 16.

Figure 12

(Color online) Schematic energy splitting of the $3d$ manifold in the PI (upper panel) and PM (lower panel) phases of ${\mathrm{V}}_2{\mathrm{O}}_3$. The correspondig $t_{2g}$ orbital occupation is ${(n_{a_{1g}},n_{e_{g1,2}^{\pi }}=0.32,0.34)}_{\mathrm{PI}}$ and ${(n_{a_{1g}},n_{e_{g1,2}^{\pi }}=0.36,0.32)}_{\mathrm{PM}}$. The renormalized values of the trigonal field are ${\Delta }_{\mathrm{PI}}=0.32\mathrm{eV}$ and ${\Delta }_{\mathrm{PM}}=-0.003\mathrm{eV}$.

Figure 13

(Color online) Orbital resolved self-energies (uper panels) and one-electron spectral function for the metallic phase of ${\mathrm{V}}_2{\mathrm{O}}_3$ for $U=3.5\mathrm{eV}$ and $J_H=1\mathrm{eV}$.