Effect of material properties on the accuracy of antiresonant approximation: Linear and second-order optical responses

Many ab initio calculations, in particular in solid state physics, rely on the antiresonant approximation. In this paper we discuss the derivation, the validity, and the accuracy of this approximation, analyzing how the optical properties of several bulk semiconducting materials and surfaces can be affected. We present accurate results for different spectroscopic quantities in the linear and nonlinear responses and we analyze the discrepancies between approximated and exact formulas. An investigation is made of the effect of the approximation on absorption spectra for different materials, showing the reliability of the approximation even in the presence of local field and excitonic effects. The energy loss is shown to be drastically affected. The effect of the band gap of materials on the quality of the approximation is also discussed. Finally, we report on the influence of the antiresonant approximation on second harmonic generation spectra.

Figure 1

Real and imaginary part of the dielectric function $\epsilon \left(\omega \right)$. Solid line: Full ab initio calculation; dashed line: AA ab initio calculation where the antiresonant term is neglected. $E_g$ is the direct band gap.

Figure 2

Imaginary part of the dielectric function $\epsilon \left(\omega \right)$ for GaAs with (a) local field effects included in the RPA and (b) excitonic effects included using the long-range kernel $(\alpha =0.2$ [6]) and a scissors of 0.8 eV [6]. Solid line: Full calculation; dashed line: AA calculation where the antiresonant term is neglected; dotted line: IPA calculation as a reference.

Figure 3

Imaginary part of the dielectric function $\epsilon \left(\omega \right)$ for AlAs with (a) local field effects included in the RPA and (b) excitonic effects included using the long-range kernel $(\alpha =0.35$ [6]) and a scissors of 0.9 eV [6]. Solid line: Full calculation; dashed line: AA calculation where the antiresonant term is neglected; dotted line: IPA calculation for reference.

Figure 4

Energy loss function for Si. Dots: Experiment [40]; dashed line: Full RPA calculation; dot-dashed line: AA RPA calculation.

Figure 5

Real part of the dielectric function $\epsilon \left(\omega \right)$ for Si. Solid line: Full RPA calculation; dashed line: AA RPA calculation.

Figure 6

Effect of the antiresonant approximation on the static dielectric value. Dots represents the RPA values for different materials considered. The solid line represents the ratio obtained analytically for IPA calculations. The direct gap refers here to the DFT direct band gap obtained from the LDA band structure, without applying any scissors operator or GW correction.

Figure 7

Real and imaginary part of the dielectric function ${\epsilon }_{yy}\left(\omega \right)$. Solid line: Full tight-binding calculation; dashed line: AA tight-binding calculation where the antiresonant term is neglected.

Figure 8

Reflectance anisotropy for the clean Si(001)$2\times 1$ surface. Solid line: Full calculation; dashed line: AA calculation where the antiresonant term is neglected. Dotted line: ${\mathrm{AA}}^{*}$ calculation as explained in the text. Spectra have been scaled by a factor as the slab contains two surfaces.

Figure 9

$|{\chi }_{xyz}|$ and $|{\chi }_{xyz}^{\mathrm{AA}}|$ for bulk GaAs (top panel), bulk AlAs (middle panel), and SiC (bottom panel). Solid line: Full calculation; dashed line: AA calculation where the antiresonant term is neglected.

Figure 10

$|{\chi }_{zxx}|$ and $|{\chi }_{zxx}^{\mathrm{AA}}|$ for the Si(001)$1\times 1$:2H (top panel) and Si(001)$2\times 1$ surfaces (bottom panel) from tight-binding calculations. Solid line: Full calculation; dashed line: AA calculation where the antiresonant term is neglected.