Role of the plasmon-pole model in the $GW$ approximation

Band gaps and band-edge energy levels are computed using the many-body perturbation theory within the $GW$ approximation, with four common plasmon pole models (PPMs) and numerical integration employed to evaluate the dynamic screening matrix. Although the Hybertsen-Louie PPM is often adopted in $GW$ calculations because it predicts band gaps best matching experimental data, we show that it is the Godby-Needs construction that agrees consistently with numerical integration on dynamic screening for materials with distinct characteristics. The variation in predicted band gaps due to different PPMs used can be as large as 1 eV in strongly localized electronic systems, and the band-edge energy levels are more sensitive to the choice of PPM than band gap even in simple semiconductors.

Figure 1

Performance of four PPMs on band gap ($E_{\mathrm{g}}$) with respect to localization length ($\sigma$) of valence electrons. Here the vertical axes are the difference in computed $E_{\mathrm{g}}$ using PPMs and numerical integration; (a) the horizontal axis is the invariant part of the localization length, and (b) it is scaled by lattice constant $a_{\mathrm{latt}}$.

Figure 2

Isosurfaces of the valence charge densities for (a) Si, (b) C, (c) Ne, and (d) ZnO. Here four valence bands for Si, C, and Ne and six for ZnO are included, and the corresponding isosurface values are set to be identical in four panels, with high to low values ranging from red (dark) to yellow (light) colors.

Figure 3

The real part of the inverse dielectric function at $\mathbf{G}={\mathbf{G}}^{\prime }=0$ along the imaginary frequency axis for (a) Si, (b) C, (c) Ne, and (d) ZnO, using the GN and HL PPMs, compared to those obtained by numerical integration.

Figure 4

The real part of the inverse dielectric function at $\mathbf{G}={\mathbf{G}}^{\prime }=0$ along the real frequency axis for (a) Si, (b) C, (c) Ne, and (d) ZnO, using the GN and HL PPMs, compared to those obtained by numerical integration.

Figure 5

The real part of the inverse dielectric function along the imaginary frequency axis for (a) Si, (b) C, (c) Ne, and (d) ZnO, using the GN and HL PPMs, compared to those obtained from numerical integration. Here $\mathbf{G}={\mathbf{G}}^{\prime }\ne 0$.

Figure 6

The real part of the inverse dielectric function along the real frequency axis for (a) Si, (b) C, (c) Ne, and (d) ZnO, using the GN and HL PPMs, compared to those obtained from numerical integration. $\mathbf{G}={\mathbf{G}}^{\prime }\ne 0$.