Towards a unified first-principles-based description of VO$_2$ using DFT+DMFT with bond-centered orbitals

Abstract

We present a combined density-functional theory and dynamical mean-field theory (DFT+DMFT) study of the full structural phase space of rutile-based vanadium dioxide (VO$_2$), including also the less studied M2 and T phases, using an unconventional bond-centered orbital basis. The use of bond-centered orbitals allows us to treat all main phases of VO$_2$, and the structural transitions between them, using one consistent approach with moderate computational cost and without pre-pattering of the structure into dimerized and undimerized V--V pairs. We obtain two distinct insulating states on the two different types of vanadium chains in the M2 phase, a singlet-insulator on the dimerized chains and a Mott-insulator on the zigzag-distorted chains, which, however, are strongly coupled in the M2 phase and thus the metal-insulator transition always occurs concomitantly for both types of sites. We also demonstrate that the M2 phase corresponds to a local energy minimum in the structural phase space of VO$_2$, the stability of which, apart from the internal structural distortion, depends crucially on the unit cell strain relative to the undistorted rutile phase. Our calculations further indicate that the symmetry-distinct triclinic T phase corresponds electronically to either an M1 or an M2-type insulator with an abrupt transition as a function of distortion. Finally, we disentangle the effect of the dimerization and zigzag distortions by constructing hypothetical structures that contain only one site type, finding that the zigzag distortion strongly favors emergence of the Mott-insulating state, both as function of distortion and on-site interaction.

Figures (8)

• Figure 1: (a) The R and (b) the M2 structures of VO$_2$ depicted in the unit cell used in this work. The short-bond pairs (SB) and zigzag-distorted chains (ZZ) are highlighted in blue and red, respectively. V (O) atoms shown in (dark) gray. (c) Distortion $\eta_1$ within the (110) plane [$\eta_2$ analogous in (11̄0) plane]. (d) The $(\eta_1, \eta_2)$ phase diagram, schematically indicating the R, M1, M2, and T phases.
• Figure 2: (a) DFT band structure of the M2 VO$_2$ shown in black together with the bands recalculated within the Wannier basis in gray. (b) Density of states (DOS) projected on V $a_{1g}$ ($e_g^\pi$) orbital character plotted in black (cyan). Orbitals on the SB (ZZ) sites shown as full (dashed) lines. (c, d) Bond-centered orbitals corresponding to the $a_{1g}$ orbitals on the (c) SB and (d) ZZ sites. Yellow (cyan) colors indicate the positive (negative) phase of the orbitals.
• Figure 3: Different local observables on the M2 (a-d) SB and (e-h) ZZ sites obtained within bond-centered DFT+DMFT as a function of $U$ and $J$: (a, e) spectral weight at zero frequency, $A(\omega=0)$, (b, f) total local occupation, (c, g) occupation of the $a_{1g}$ orbital, and (d, h) the $a_{1g}$ quasiparticle weight $Z$. Labels (1-3) indicate the different regimes discussed in the text. Black-filled stars indicate the cRPA values of $(U, J)$ obtained for the R phase in Mlkvik_et_al:2024, while white-filled stars indicate the values used in subsequent calculations.
• Figure 4: Local spectral functions in M2 VO$_2$ at $(U, J)=(2.0,0.1)$ eV for the (a) SB and (b) ZZ sites. Black (cyan) lines show the $a_{1g}$ ($e_g^\pi$) bands, gray line shows the total per impurity. Dashed line indicates the Fermi level.
• Figure 5: Selected observables calculated as function of structural distortion interpolating between (a-c) R and M2, and (d-f) M2 and M1 (through T) structures for the SB (solid line, filled circles) and ZZ (dashed line, open circles) sites. (a, d) Spectral weight at zero frequency. (b, e) Orbital occupation of the $a_{1g}$ (black) and the two $e_g^\pi$ (cyan) orbitals. (c, f) Total energy relative to the R phase.