Covalency in transition-metal oxides within all-electron dynamical mean-field theory

A combination of dynamical mean field theory and density functional theory, as implemented by Haule et al. [Phys. Rev. B 81, 195107 (2010)], is applied to both the early and late transition metal oxides. For a fixed value of the local Coulomb repulsion, without fine tuning, we obtain the main features of these series, such as the metallic character of ${\mathrm{SrVO}}_3$ and the insulating gaps of ${\mathrm{LaVO}}_3$, ${\mathrm{LaTiO}}_3$, and ${\mathrm{La}}_2{\mathrm{CO}}_4$, which are in good agreement with experiment. This study highlights the importance of local physics and high energy hybridization in the screening of the Hubbard interaction and how different low energy behaviors can emerge from the unified treatment of the transition metal series.

Figure 1

The total DOS and its projection to the $3d$ ion for selected transition metal oxides. Experimental photoemission for ${\mathrm{SrVO}}_3$, ${\mathrm{LaVO}}_3$, ${\mathrm{LaTiO}}_3$, and ${\mathrm{La}}_2{\mathrm{CuO}}_4$ is plotted by black dots, and was digitized from Refs. [81, 82, 83, 84], respectively.

Figure 2

Zoom-in of the low-energy DOS projected to the $3d$ orbitals for insulating compounds. For clarity, the curves were offset for 0.07/eV. The arrows mark the experimental size of the gap.

Figure 3

The dependence of the electronic structure of ${\mathrm{SrVO}}_3$ on the value of the local Coulomb repulsion $U$ in this all-electron calculation. The text displays the valence of the ${\mathrm{V}}^{4+}$ ion. The thick line presents the total DOS and the thin line its projection to the $3d$-ion subset. For clarity, the different electronic structures are offset for 3 eV.

Figure 4

The electronic structure of ${\mathrm{LaVO}}_3$ for different values of the local Coulomb repulsion $U$. We also display the valence of the ${\mathrm{V}}^{3+}$ ion.

Figure 5

The electronic structure of ${\mathrm{LaTiO}}_3$ for different values of the local Coulomb repulsion $U$. We also display the valence of the ${\mathrm{Ti}}^{3+}$ ion.

Figure 6

The electronic structure of ${\mathrm{La}}_2{\mathrm{CuO}}_4$ for different values of the local Coulomb repulsion $U$. We also display the valence of the ${\mathrm{Cu}}^{2+}$ ion.

Figure 7

Orbitally resolved DOS for ${\mathrm{La}}_2{\mathrm{CuO}}_4$ at $U=10$ eV. The total $3d$ and total oxygen-$p$ DOS is offset for 0.25/eV.

Figure 8

The imaginary part of the impurity hybridization function for various materials at $U=10$ eV. We also display what is the dominant source of various peaks in the hybridization function.

Figure 9

The total DOS and its projection to the $3d$ ion within DFT+DMFT for insulating transition metal oxides, computed using standard fully localized limit double counting and fixed $U=10$ eV and $J_{\text{Hunds}}=0.7$ eV. Experimental photoemission is the same as in Fig. 1.

Figure 10

The $3d$ density of states within DFT+DMFT for ${\mathrm{La}}_2{\mathrm{CuO}}_4$ using the three different methodologies explained in Table 1.

Figure 11

The radial dependence of the function $\varphi \left(r\right)$, which defines the projector to the correlated $3d$ set of orbitals. Three different projectors [Proj(1), Proj(2), and Proj(3)] are defined in the upper panel. Lower panel shows the density of states within LDA for ${\mathrm{La}}_2{\mathrm{CuO}}_4$ using the three different projectors defined in the upper panel.