GW quasiparticle band gap of the hybrid organic-inorganic perovskite CH$_3$NH$_3$PbI$_3$: Effect of spin-orbit interaction, semicore electrons, and self-consistency

TL;DR

This study uses many-body perturbation theory to analyze the quasiparticle band gap of CH$_3$NH$_3$PbI$_3$, highlighting the effects of spin-orbit interaction, semicore electrons, and self-consistency, resulting in a more accurate theoretical prediction aligned with experiments.

Contribution

The paper provides a systematic analysis of factors affecting the GW band gap of CH$_3$NH$_3$PbI$_3$, resolving previous inconsistencies and improving theoretical accuracy.

Findings

Semicore states increase the band gap by 0.2 eV.

Self-consistency raises the band gap by 0.4 eV.

Most accurate band gap estimate is 1.65 eV, matching experimental optical gap.

Abstract

We study the quasiparticle band gap of the hybrid organic-inorganic lead halide perovskite CH$_3$NH$_3$PbI$_3$, using many-body perturbation theory based on the $GW$ approximation. We perform a systematic analysis of the band gap sensitivity to relativistic spin-orbit effects, to the description of semicore Pb-5$d$ and I-4$d$ electrons, and to the starting Kohn-Sham eigenvalues. We find that the inclusion of semicore states increases the calculated band gap by 0.2 eV, and self-consistency on the quasiparticle eigenvalues using a scissor correction increases the band gap by 0.4 eV with respect to the $G_0W_0$ result. These findings allow us to resolve an inconsistency between previously reported $GW$ calculations for CH$_3$NH$_3$PbI$_3$. Our most accurate band gap is 1.65 eV, and is in good agreement with the measured optical gap after considering a small excitonic shift as determined in experiments.