All-electron quasiparticle self-consistent <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi mathvariant="italic">GW</mml:mi></mml:math> band structures for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>SrTiO</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:math> including lattice polarization corrections in different phases

Abstract

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 $0.8\mathrm{\ensuremath{\Sigma}}$ approach, the gap is still overestimated. The $0.8\mathrm{\ensuremath{\Sigma}}$ approach is discussed and justified in terms of various recent literature results including electron-hole corrections. Adding a lattice polarization correction (LPC) in the $\mathbf{q}\ensuremath{\rightarrow}0$ 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.