G0W0band gap of ZnO: Effects of plasmon-pole models

Abstract

Carefully converged calculations are performed for the band gap of ZnO within many-body perturbation theory (G 0 W 0 approximation). The results obtained using four different well-established plasmon-pole models are compared with those of explicit calculations without such models (the contour-deformation approach). This comparison shows that, surprisingly, plasmon-pole models depending on the f -sum rule gives less precise results. In particular, it confirms that the band gap of ZnO is underestimated in the G 0 W 0 approach as compared to experiment, contrary to the recent claim of Shih et al.

Band-structure calculations for the 3dtransition metal oxides inGW

“…[34]), that is considered to be reliable in main group compounds [15] gives a much too large band gap of 4.0 eV in Fe 2 O 3 [31], compared to the experimental gap at 2.1 eV [35]. The G 0 W 0 (LDA) variant, which underestimates the gap of ZnO by as much as 1 eV [7,22], already overestimates the gap by 0.3 eV in TiO 2 [30] and by 0.6 eV in SrTiO 3 [36]. The self-consistency in the wave-functions was found to be essential for the correct band-structure of Cu 2 O [24,28], but in ZnO and GaN, the self-consistency did not correct the underbinding of the 3d states [13,37].…”

“…The past decade has seen considerable developments and discussions around a number of issues related to the GW method; concerning the technical implementation, such as pseudo-potential vs all electron methods [16,18], the issue of core-valence partitioning [12,16,19] and pseudopotential scattering properties at high energies [20]; concerning convergence parameters, such as the number of unoccupied bands [21,22]; concerning approximations for the screened Coulomb interaction W, such as the plasmon pole model [22], the random phase approximation (RPA) [14], or vertex corrections and excitonic effects beyond RPA [13,23]; and concerning the degree of self-consistency of both the eigenenergies and the wave-functions [9,11,12,13,14,24].…”

GWcalculations using the spectral decomposition of the dielectric matrix: Verification, validation, and comparison of methods

“…6,[19][20][21] This approximation not only reduces the computational workload, but also provides an analytical expression for the self-energy as a function of frequency. However, it has been shown that results obtained with different plasmonpole models may be significantly different, 8,22 and thus it is important to develop efficient techniques to explicitly take into account the frequency dependence of W .…”

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

“…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. 34 Parallel to these developments, different approaches were proposed to circumvent or at least alleviate the convergence problem.…”

“…If the cutoff energy is not chosen as in Eq. (33) in the center but elsewhere in the interval between the states with quantum numbers L cut − 1 and L cut , then the formulas for all ∆ ℓ are modified by an additional identical term proportional to E −3/2 cut . As a visualization, Fig.…”