Full orbital calculation scheme for materials with strongly correlated electrons

We propose a computational scheme for the ab initio calculation of Wannier functions (WFs) for correlated electronic materials. The full-orbital Hamiltonian $\widehat{H}$ is projected into the WF subspace defined by the physically most relevant partially filled bands. The Hamiltonian ${\widehat{H}}^{WF}$ obtained in this way, with interaction parameters calculated by constrained local-density approximation (LDA) for the Wannier orbitals, is used as an ab initio setup of the correlation problem, which can then be solved by many-body techniques, e.g., dynamical mean-field theory (DMFT). In such calculations the matrix self-energy $\widehat{\mathrm{\sum }}\left(\epsilon \right)$ is defined in WF basis which then can be converted back into the full-orbital Hilbert space to compute the full-orbital interacting Green function $G(\mathbf{r},{\mathbf{r}}^{\prime },\epsilon )$. Using $G(\mathbf{r},{\mathbf{r}}^{\prime },\epsilon )$ one can evaluate the charge density, modified by correlations, together with a new set of WFs, thus defining a fully self-consistent scheme. The Green function can also be used for the calculation of spectral, magnetic, and electronic properties of the system. Here we report the results obtained with this method for $\mathrm{Sr}\mathrm{V}{\mathrm{O}}_3$ and ${\mathrm{V}}_2{\mathrm{O}}_3$. Comparisons are made with previous results obtained by the LDA+DMFT approach where the LDA density of states was used as input, and with new bulk-sensitive experimental spectra.

Figure 1

Scheme of the ab initio fully self-consistent LDA+DMFT scheme based on the WF formalism (see text).

Figure 2

Comparison of $\mathrm{V}\text{−}3d\left(t_{2g}\right)$ spectral functions for $\mathrm{Sr}\mathrm{V}{\mathrm{O}}_3$ calculated via LDA+DMFT (QMC) using: LDA DOS—light line; projected Hamiltonian—black line. The Fermi level corresponds to zero.

Figure 3

Comparison of $\mathrm{V}\text{−}3d\left(t_{2g}\right)$ spectral functions for ${\mathrm{V}}_2{\mathrm{O}}_3$ in the metallic phase calculated via LDA+DMFT (QMC) using: LDA DOS (LMTO)—light line (Ref. 44); LDA DOS (ASW)—dashed line; projected Hamiltonian—black line. The Fermi level corresponds to zero.

Figure 4

Comparison of $\mathrm{V}\text{−}3d\left(t_{2g}\right)$ spectral functions for ${\mathrm{V}}_2{\mathrm{O}}_3$ in the insulating phase calculated via LDA+DMFT (QMC) using: LDA DOS—light line; projected Hamiltonian—black line. Upper figures—$a_{1g}$; lower figures—$e_g^{\pi }$ orbitals. The Fermi level corresponds to zero.

Figure 5

Comparison of $\mathrm{V}\text{−}3d\left(t_{2g}\right)$ spectral functions for ${\mathrm{V}}_2{\mathrm{O}}_3$ in the metal phase calculated via LDA+DMFT (QMC) using: LDA DOS—light line; projected Hamiltonian—black line. Upper figures—$a_{1g}$; lower figures—$e_g^{\pi }$ orbitals. The Fermi level corresponds to zero.

Figure 6

Self-energy on real energy axis for $\mathrm{Sr}\mathrm{V}{\mathrm{O}}_3$. Real part—full black line; imaginary part—full light line. The Fermi level corresponds to zero.

Figure 7

Comparison of total spectral functions of $\mathrm{Sr}\mathrm{V}{\mathrm{O}}_3$ calculated via: LDA—full light line; using the full-orbital self-energy from LDA+DMFT (QMC)—dashed black line. The Fermi level corresponds to zero.

Figure 8

Partial $\mathrm{V}\text{−}3d$ spectral functions for $\mathrm{Sr}\mathrm{V}{\mathrm{O}}_3$ calculated using the full-orbital self-energy from LDA+DMFT (QMC). Total $d$—full light line; $t_{2g}$—full black line; $e_g$—dashed black line. The Fermi level corresponds to zero.

Figure 9

Comparison of photoemission spectra of $\mathrm{Sr}\mathrm{V}{\mathrm{O}}_3$ with spectral functions calculated via LDA+DMFT (QMC): taking into account only $t_{2g}$—light line; using full-orbital self-energy—black line. Theoretical spectra are multplied with the Fermi function corresponding to 20 K and broadened with a 0.2-eV Gaussian to account for the instrumental resolution. Intensities are normalized to yield the same height for the quasiparticle peaks. The Fermi level corresponds to zero.

Figure 10

Self-energy on real energy axis for ${\mathrm{V}}_2{\mathrm{O}}_3$. Real part of the self-energy from LDA+DMFT (QMC)—full black line; imaginary part—full light line. The Fermi level corresponds to zero.

Figure 11

Comparison of total spectral functions of ${\mathrm{V}}_2{\mathrm{O}}_3$ calculated via: LDA—full light line; using full-orbital self-energy from LDA+DMFT (QMC)—dashed black line. The Fermi level corresponds to zero.

Figure 12

Partial $\mathrm{V}\text{−}3d$ spectral functions for ${\mathrm{V}}_2{\mathrm{O}}_3$ calculated using full-orbital self-energy from LDA+DMFT (QMC). Total $d$—full light line; $t_{2g}$—full black line; $e_g$—dashed black line. The Fermi level corresponds to zero.

Figure 13

Comparison of photoemission spectra of ${\mathrm{V}}_2{\mathrm{O}}_3$ with spectral functions calculated via LDA+DMFT (QMC): taking into account only $t_{2g}$—light line; using full-orbital self-energy—black line. Theoretical spectra are multiplied with the Fermi function and broadened with a 0.2-eV Gaussian to simulate instrumental resolution. Intensities are normalized for peaks situated around −1 eV. The Fermi level corresponds to zero.

Figure 14

Comparison of $\mathrm{O}\text{−}1s\to 2p$ x-ray-absorption spectroscopy (XAS) spectra of ${\mathrm{V}}_2{\mathrm{O}}_3$ with spectral functions calculated via LDA+DMFT (QMC) using full-orbital self-energy. Theoretical spectra are multiplied with the Fermi function and broadened with a 0.2-eV Gaussian to simulate instrumental resolution. Intensities of the theory curves are normalized to the correct number of $\mathrm{V}\text{−}3d$ electrons in the unit cell (eight electrons). The experimental curve is normalized to the same peak height as the full orbital curve. The Fermi level corresponds to zero.