Quasiparticle Band Gap of ZnO: High Accuracy from the ConventionalG0W0Approach

Abstract

Contrary to previous reports, we show that the conventional GW (the so-called G⁰W⁰) approximation can be used to calculate accurately the experimental band gap (∼3.6 eV) of ZnO. The widely discussed underestimate of the quasiparticle gap of ZnO within the GW method is a result of an inadequate treatment of the semicore electrons and the slow and nonuniform convergence in the calculation of the Coulomb-hole self-energy in previous studies. In addition, an assumed small kinetic energy cutoff for the dielectric matrix may result in a false convergence behavior for the quasiparticle self-energy.

Improving accuracy and efficiency of calculations of photoemission spectra within the many-body perturbation theory

“…12 However an approach that is at the same time efficient, and thus applicable to systems with several hundred electrons, and whose numerical accuracy may be systematically controlled, is not yet available.…”

Analytic evaluation of the electronic self-energy in theGWapproximation for two electrons on a sphere

“…The dashed lines indicate the asymptotic expansions Σ c ℓ (ǫ ℓ ) + ∆ ℓ (E cut ), where the analytic expressions for ∆ 0 and ∆ 1 from Eqs. (32) and (34) with terms up to the order E −3/2 cut are used. The difference Z 1Σ c 1 (ǫ 1 ) − Z 0Σ c 0 (ǫ 0 ), which equals the contribution of the correlation part of the self-energy to the gap, is also shown together with the asymptotic formula…”

“…Furthermore, the restricted Hilbert space does not allow us to address problems like the convergence behavior with respect to the number of empty states. 32 Peculiar symmetries, such as that between occupied and unoccupied states in the two-site model at half filling, 43 which are not obeyed by real solids, may also have an influence on the results. For completeness, it should be mentioned that the polaron model of individual electrons coupled to an external boson field can also be treated analytically, 48 but its usefulness as a test system for the GW approximation is even more limited, as there is no explicit renormalizable electron-electron interaction.…”

“…It was subsequently argued that this peculiar behavior was caused by the particular choice of plasmon-pole model used in Ref. 32 and that far fewer bands are in fact required if the full frequency-dependent screening function is properly constructed within the random-phase approximation. 33 However, a similarly slow convergence was again observed in an all-electron calculation for zinc oxide that not only avoided plasmon-pole models but also the additional pseudopotential approximation.…”

“…Much attention was raised after an early all-electron calculation, 12 which claimed much smaller semiconductor band gaps than established pseudopotential results, was put into question due to alleged incomplete convergence with respect to this parameter, 29,30 leading to further detailed studies 22,28,31 that illustrated the slow convergence rate of the quasiparticle energies for a wide variety of materials. As an extreme example, Shih et al 32 reported that bulk zinc oxide required thousands of unoccupied bands to achieve satisfactory accuracy in a calculation based on pseudopotentials and a plane-wave basis set. It was subsequently argued that this peculiar behavior was caused by the particular choice of plasmon-pole model used in Ref.…”