Quasiparticle Band Gap of ZnO: High Accuracy from the Conventional $G^0{W}^0$ Approach

Contrary to previous reports, we show that the conventional $GW$ (the so-called $G^0{W}^0$) approximation can be used to calculate accurately the experimental band gap ($\sim 3.6\mathrm{eV}$) 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.

Figure 1

The LDA (left panels) and $\mathrm{LDA}+U$ (right panels) band structures of ZnO. Projection of the band wave functions onto O $2p$ (top panels) and Zn $3d$ (bottom panels) orbitals are shown as vertical bars superimposed on the band structure.

Figure 2

Quasiparticle band gap of ZnO as a function of the number of conduction bands included in the Coulomb-hole self-energy calculation with a high cutoff energy (80 Ry) for the dielectric function as discussed in the text.

Figure 3

Coulomb-hole self-energies of the VBM and CBM of ZnO as a function of the number of conduction bands included in the calculation, showing the different convergence behavior between the CBM and the VBM.

Figure 4

Wave functions of CBM, VBM, and a Zn $3d$ state in the momentum space.

Figure 5

Quasiparticle band gap of ZnO calculated within the $\mathrm{LDA}+U/GW$ method and with different dielectric matrix cutoffs, showing the false convergence behavior of the band gap when a small cutoff energy is used.