Covalency and the metal-insulator transition in titanate and vanadate perovskites

A combination of density functional and dynamical mean-field theory is applied to the perovskites ${\mathrm{SrVO}}_3$, ${\mathrm{LaTiO}}_3$, and ${\mathrm{LaVO}}_3$. We show that DFT + DMFT in conjunction with the standard fully localized-limit (FLL) double-counting predicts that ${\mathrm{LaTiO}}_3$ and ${\mathrm{LaVO}}_3$ are metals even though experimentally they are correlation-driven (“Mott”) insulators. In addition, the FLL double counting implies a splitting between oxygen $p$ and transition metal $d$ levels, which differs from experiment. Introducing into the theory an ad hoc double counting correction, which reproduces the experimentally measured insulating gap leads also to a $p$-$d$ splitting consistent with experiment if the on-site interaction $U$ is chosen in a relatively narrow range ($\sim$$6\pm 1$ eV). The results indicate that these early transition metal oxides will serve as critical test for the formulation of a general ab initio theory of correlated electron metals.

Figure 1

(a) Density of states from DFT calculation of ${\mathrm{SrVO}}_3$. (b)–(d) Positive half-plane: spectral functions for the $e_g$, $t_{2g}$, and oxygen $p$ bands of ${\mathrm{SrVO}}_3$ obtained from fully charge self-consistent FLL-double counting DFT + DMFT calculations. Negative half-plane: spectral functions obtained from “one-shot” calculations without full charge self-consistency but with $d$-level energies adjusted so that the $d$ occupancies are within $0.01$ of the values found in the corresponding fully charge self-consistent calculations. The dotted curve (blue online) is the experimental spectra reproduced from Ref. [31].

Figure 2

The MIT phase diagrams for ${\mathrm{LaTiO}}_3$ and ${\mathrm{LaVO}}_3$. The solid (dashed) lines are phase boundary and DFT $N_d$ for tilted (cubic) structure. Open symbols represent metallic solutions, closed symbols are insulating solutions.

Figure 3

Noninteracting density of states calculated using the Quantum Espresso implementation of the GGA approximation (with “DFT” label) and spectral functions $A\left(\omega \right)$ (solid curves) for ${\mathrm{LaTiO}}_3$ [(a) blue online] and ${\mathrm{LaVO}}_3$ [(b) red online] using the experimental lattice structure at $J=0.65\text{eV}$ for $U$-values indicated, with $\Delta$ adjusted to match the insulating gap. The vertical dashed line marks the Fermi level. Black dashed curves give the experimentally determined oxygen density of states, reproduced from Refs. [3, 38]. For ${\mathrm{LaTiO}}_3$, the $(U,N_d)$ pairs are $(3.7,1.07)$, $(5.0,1.3)$, and $(9.0,1.5)$ with the band $N_d$ being $1.56$. For ${\mathrm{LaVO}}_3$, we have $(3.7,2.05)$, $(5.0,2.30)$, and $(9.0,2.45)$ with the DFT value of $N_d$ being $2.55$.