Fully relativistic $GW$/Bethe-Salpeter calculations in BerkeleyGW: implementation, symmetries, benchmarking, and performance

Abstract

Computing the $GW$ quasiparticle bandstructure and Bethe-Salpeter Equation (BSE) absorption spectra for materials with spin-orbit coupling has commonly been done by treating $GW$ corrections and spin-orbit coupling as separate perturbations to density-functional theory. However, accurate treatment of materials with strong spin-orbit coupling often requires a fully relativistic approach using spinor wavefunctions in the Kohn-Sham equation and $GW$/BSE. Such calculations have only recently become available, in particular for the BSE. We have implemented this approach in the plane-wave pseudopotential $GW$/BSE code BerkeleyGW, which is highly parallelized and widely used in the electronic-structure community. We present reference results for quasiparticle bandstructures and optical absorption spectra of solids with different strengths of spin-orbit coupling, including Si, Ge, GaAs, GaSb, CdSe, Au, and Bi${}_2$Se${}_3$. The calculated quasiparticle band gaps of these systems are found to agree with experiment to within a few tens of meV. The absorption spectrum of GaSb calculated with the fully-relativistic $GW$-BSE captures the large spin-orbit splitting of peaks in the spectrum. For Bi${}_2$Se${}_3$, we find a drastic change in the low-energy bandstructure compared to that of DFT, with the fully-relativistic treatment of the $GW$ approximation correctly capturing the parabolic nature of the valence and conduction bands after including off-diagonal self-energy matrix elements. We present the detailed methodology, approach to spatial symmetries for spinors, comparison against other codes, and performance compared to spinless $GW$/BSE calculations and perturbative approaches to SOC. This work aims to spur further development of spinor $GW$/BSE methodology in excited-state research software.

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• Exchange-Driven Intermixing of Bulk and Topological Surface State by Chiral Excitons in Bi2Se3
• Effects of self-consistent extended Hubbard interactions and spin-orbit couplings on energy bands of semiconductors and topological insulators
• Spin-dependent interactions in orbital-density-dependent functionals: non-collinear Koopmans spectral functionals
• High-fidelity electronic structure and properties of InSb: $G_0{W}_0$ and Bayesian-optimized hybrid functionals and DFT+$U$ approaches
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