Polarization-dependent density-functional theory and quasiparticle theory: Optical response beyond local-density approximations
| Autor: | John W. Wilkins, Wilfried G. Aulbur, Lars Jönsson |
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| Rok vydání: | 1996 |
| Předmět: | |
| Zdroj: | Physical Review B. 54:8540-8550 |
| ISSN: | 1095-3795 0163-1829 |
| Popis: | The polarization (P) dependence of the exchange-correlation energy (${\mathit{E}}_{\mathit{xc}}$) of semiconductors results in an effective field (${\mathrm{\ensuremath{\partial}}}^{2}$${\mathit{E}}_{\mathit{xc}}$/\ensuremath{\partial}${\mathit{P}}^{2}$)P\ensuremath{\equiv}${\ensuremath{\gamma}}_{1}$P in the Kohn-Sham equations [Gonze et al., Phys. Rev. Lett 74, 4035 (1995)]. This effective field is absent in local-density approximations such as LDA and GGA. We show that in the long-wavelength limit ${\ensuremath{\gamma}}_{1}$\ensuremath{\simeq}${\mathrm{\ensuremath{\chi}}}_{\mathit{LDA}}^{\mathrm{\ensuremath{-}}1}$-${\mathrm{\ensuremath{\chi}}}_{\mathit{expt}}^{\mathrm{\ensuremath{-}}1}$ where \ensuremath{\chi} is the linear susceptibility. We find that ${\ensuremath{\gamma}}_{1}$ scales roughly linearly with average bond length suggesting a simple, weakly material-dependent function ${\mathit{E}}_{\mathit{xc}}$[P]. For medium-gap group IV and III-V semiconductors ${\ensuremath{\gamma}}_{1}$ is remarkably constant: ${\ensuremath{\gamma}}_{1}$=-0.25\ifmmode\pm\else\textpm\fi{}0.05. Using the average LDA band gap mismatch \ensuremath{\Delta} and the average quasiparticle gap ${\mathit{E}}_{\mathit{g}}$ a simplified quasiparticle approach yields ${\mathrm{\ensuremath{\chi}}}_{\mathit{LDA}}^{\mathrm{\ensuremath{-}}1}$-${\mathrm{\ensuremath{\chi}}}_{\mathit{QP}}^{\mathrm{\ensuremath{-}}1}$\ensuremath{\simeq}-\ensuremath{\Delta}/(${\mathit{E}}_{\mathit{g}}$\ensuremath{\chi})=-0.27 *0.10 in good agreement with the value of ${\ensuremath{\gamma}}_{1}$. However, for materials containing first-row elements (B,C,N,O) ${\ensuremath{\gamma}}_{1}$ varies by a factor of 2 while \ensuremath{\Delta}/(${\mathit{E}}_{\mathit{g}}$\ensuremath{\chi}) is roughly constant. That is, the simple quasiparticle estimate fails to reproduce the polarization dependence of ${\mathit{E}}_{\mathit{xc}}$[P]. For nonlinear response functions, an analysis of ${\mathit{E}}_{\mathit{xc}}$[P] leads to Miller-like expressions ${\mathrm{\ensuremath{\chi}}}_{\mathit{expt}}^{(\mathit{n})}$\ensuremath{\simeq}[${\mathrm{\ensuremath{\chi}}}_{\mathit{expt}}$/${\mathrm{\ensuremath{\chi}}}_{\mathit{LDA}}$${]}^{\mathit{n}+1\phantom{\rule{0ex}{0ex}}}$${\mathrm{\ensuremath{\chi}}}_{\mathit{LDA}}^{(\mathit{n})}$, n= 2, 3, where the formula for ${\mathrm{\ensuremath{\chi}}}^{(3)}$ is valid only when ${\mathrm{\ensuremath{\chi}}}^{(2)}$=0. For ${\mathrm{\ensuremath{\chi}}}^{(2)}$, this estimate works well for all the materials including those containing first-row elements. \textcopyright{} 1996 The American Physical Society. |
| Databáze: | OpenAIRE |
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