All-electron quasi-particle self-consistent $GW$ band structures for SrTiO$_3$ including lattice polarization corrections in different phase

TL;DR

This study employs all-electron QS$GW$ calculations with lattice polarization corrections to accurately determine the band structure of SrTiO$_3$, addressing overestimation issues and comparing different phases.

Contribution

It introduces a comprehensive all-electron QS$GW$ approach with lattice polarization corrections for SrTiO$_3$, improving agreement with experimental band gaps across different structural phases.

Findings

Lattice polarization correction significantly improves band gap agreement with experiment.

The 0.8$oldsymbol{ extSigma}$ correction partially addresses screening underestimation.

The LDA to $GW$ gap correction is nearly structure-independent.

Abstract

The electronic band structure of SrTiO$_3$ is investigated in the all-electron QS$GW$ approximation. Unlike previous pseudopotential based QS$GW$ or single-shot $G_0W_0$ 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$\Sigma$ approach, the gap is still overestimated. The 0.8$\Sigma$ approach is discussed and justified in terms of various recent literature results including electron-hole corrections. Adding a lattice polarization correction (LPC) in the ${\bf q}\rightarrow0$ 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 post-perovskite structure and find that the LDA (local density approximation) to $GW$ gap correction is almost independent of structure.