Dipole matrix element approach versus Peierls approximation for optical conductivity

We develop a computational approach for calculating the optical conductivity in the augmented plane-wave basis set of wien2k and apply it for thoroughly comparing the full dipole matrix element calculation and the Peierls approximation. The results for SrVO${}_3$ and V${}_2$O${}_3$ show that the Peierls approximation, which is commonly used in model calculations, works well for optical transitions between the $d$ orbitals. In a typical transition-metal oxide, these transitions are solely responsible for the optical conductivity at low frequencies. The Peierls approximation does not work, on the other hand, for optical transitions between $p$ and $d$ orbitals which usually became important at frequencies of a few eVs.

Figure 1

Noninteracting partial density of states of SrVO${}_3$ (results abbreviated as LDA) compared to DMFT spectra at $T=1160\mathrm{K}$. Two DMFT basis sets were employed: first, the three orbital $t_{2g}$ basis with parameters $(U,J,V)=(5.05,0.75,3.55)$ eV; second, the entire V-$d$ manifold with the same interaction parameters for all orbitals.

Figure 2

Optical conductivity of SrVO${}_3$ calculated with dipole matrix elements and the Peierls approximation, respectively, compared to experiment (Ref. 66).

Figure 3

Optical conductivity of SrVO${}_3$ comparing LDA, DMFT, and experiment. The LDA and DMFT results were computed by the dipole matrix element approach (bottom). The top panel shows the sum rule $N_{\mathrm{eff}}\left({\Omega }_c\right)$ from Eq. (12) for $\sigma$ of the lower panel (the experimental data are from Ref. 66).

Figure 4

Optical conductivity of V${}_2$O${}_3$ ($\alpha$ phase, metallic) at $T=460$ K calculated with dipole matrix elements [(a) LDA, (b) DMFT for V-$t_{2}g$ with $(U,J,V)=(4,0.7,2.6)$ eV] and the Peierls approximation [(c) LDA, (d) DMFT for V-$t_{2}g$ with $(U,J,V)=(4,0.7,2.6)$ eV], respectively, compared to experiment (dashed line taken from Ref. 79).