All-electron quasiparticle self-consistent $\mathit{GW}$ band structures for ${\mathrm{SrTiO}}_3$ including lattice polarization corrections in different phases

The electronic band structure of ${\mathrm{SrTiO}}_3$ is investigated in the all-electron quasiparticle self-consistent $\mathit{GW}$ ($\mathrm{QS}\mathit{GW}$) approximation. Unlike previous pseudopotential-based $\mathrm{QS}\mathit{GW}$ or single-shot $G_0{W}_0$ calculations, the gap is found to be significantly overestimated compared to experiment. After putting in a correction for the underestimate of the screening by the random phase approximation in terms of a $0.8\mathrm{\Sigma }$ approach, the gap is still overestimated. The $0.8\mathrm{\Sigma }$ approach is discussed and justified in terms of various recent literature results including electron-hole corrections. Adding a lattice polarization correction (LPC) in the $\mathbf{q}\to 0$ limit for the screening of $W$, agreement with experiment is recovered. The LPC is alternatively estimated using a polaron model. We apply our approach to the cubic and tetragonal phases as well as a hypothetical layered postperovskite structure and find that the local density approximation (LDA) to $\mathit{GW}$ gap correction is almost independent of structure.

Figure 1

$\mathrm{QS}\mathit{GW}$ (blue) and LDA (red) optical dielectric constant ${\epsilon }_{\infty }$ compared to experiment. Experimental data for $\mathit{GW}$(T) is taken at room temperature; for $\mathit{GW}$(0), 0 K data is used. LDA data for NiO is not shown because it is off the scale; similarly for the narrow-gap semiconductors InAs, GaSb, InSb, and Ge where the LDA gap is negative. The dotted line would indicate perfect agreement between calculation and experiment, while the dashed line corresponds to a 20% underestimate by the calculation.

Figure 2

Crystal structures of ${\mathrm{SrTiO}}_3$ (a) cubic, (b) tetragonal $I4/mcm$, and (c) layered orthorhombic ${\mathrm{CaIrO}}_3$ view from the $z$ axis.

Figure 3

Band structure of (a) cubic, (b) tetragonal ${\mathrm{SrTiO}}_3$, and (c) layered orthorhombic. LDA: blue dashed lines; $\mathrm{QS}\mathit{GW}$: red solid lines.

Figure 4

Comparison of the band structure of ${\mathrm{SrTiO}}_3$ in $\mathrm{QS}\mathit{GW}$ (red dashed lines) and in $\mathrm{QS}\mathit{GW}$ with lattice polarization correction using the BM approach with $4\times 4\times 4$ mesh (blue solid lines).