Role of nonlocal exchange in the electronic structure of correlated oxides

We present a systematic study of the electronic structure of several prototypical correlated transition-metal oxides: VO${}_2$, V${}_2$O${}_3$, Ti${}_2$O${}_3$, LaTiO${}_3$, and YTiO${}_3$. In all these materials, in the low-temperature insulating phases the local and semilocal density approximations (LDA and GGA, respectively) of density-functional theory yield a metallic Kohn-Sham band structure. Here we show that, without invoking strong-correlation effects, the role of nonlocal exchange is essential to cure the LDA/GGA delocalization error and provide a band-structure description of the electronic properties in qualitative agreement with the experimental photoemission results. To this end, we make use of hybrid functionals that mix a portion of nonlocal Fock exchange with the local LDA exchange-correlation potential. Finally, we discuss the advantages and the shortcomings of using hybrid functionals for correlated transition-metal oxides.

Figure 1

Densities of states of insulating VO${}_2$ obtained with the hybrid functional of Eq. (4) according to different choices of the mixing parameter $\alpha$ and the screening parameter $\mu$. In (a) the topmost panel corresponds to the LDA. In the other panels $\mu =0.2$ Å${}^{-1}$ and $\alpha$ is raised up to 0.5. In (b) $\alpha$ is fixed to 0.25 and the results are obtained for different values of $\mu$. Here, and in all the following figures, the Fermi energy for insulators is set in the midpoint of the band gap.

Figure 2

Comparison of the calculated density of states of (upper panel) insulating monoclinic and (bottom panel) metallic rutile phases of VO${}_2$ with the experimental photoemission spectra from Ref. 46. The MIT is correctly reproduced by the LDA-HSE06 hybrid functional, while the LDA DOS is always metallic.

Figure 3

Density of states of monoclinic insulating V${}_2$O${}_3$, calculated both in the LDA and LDA-HSE06, according to the different considered magnetic structures. The magnetic order is visualized in the insets to each panel, where the light blue circles schematically represent V atoms in the (distorted) hexagonal planes that characterize the monoclinic crystal structure and the arrows display the directions of the local magnetic moments.

Figure 4

Comparison between the DOSs calculated in the LDA and LDA-HSE06 and the experimental photoemission spectra from Ref. 60. (a) Antiferromagnetic insulating phase and (b) paramagnetic metallic phases of V${}_2$O${}_3$.

Figure 5

(a) LDA and LDA-HSE06 densities of states (upper and bottom panels, respectively), together with the DOSs projected onto Ti $s$, Ti $d$, and O$p$ states, for insulating Ti${}_2$O${}_3$ at room temperature. (b) Comparison of the total DOS in the LDA and HSE06 with the XPS spectrum from Ref. 67.

Figure 6

Comparison between the LDA and LDA-HSE06 DOSs and Ti $s$, Ti $d$, and O $p$ projected DOSs, calculated for metallic Ti${}_2$O${}_3$ at $T=868$ K.

Figure 7

(a) DOS and projected DOS for LaTiO${}_3$ calculated in the LDA and LDA-HSE06 and (b) comparison with experimental photoemission spectra from Ref. 83.

Figure 8

(a) DOS and projected DOS for YTiO${}_3$ calculated in the LDA and LDA-HSE06 and (b) comparison with experimental photoemission spectra from Ref. 83.