Linear optical response in silicon and germanium including self-energy effects

Abstract

We calculate the optical response of silicon, ${\ensuremath{\epsilon}}_{1}$(\ensuremath{\omega}), below the optical-absorption threshold and the static dielectric constant of germanium. The time-dependent local-density approximation (LDA) is modified by the addition of a self-energy term taken to be a ``scissors operator,'' ${P}_{c\mathrm{k}}$${\ensuremath{\Delta}}_{\mathrm{k}}$. This form leads to a Ward identity replacement p\ensuremath{\rightarrow}(${\ensuremath{\epsilon}}_{n\mathrm{k}}$-${H}_{\mathrm{k}}^{\mathrm{LDA}{)}^{\ensuremath{-}1}}$ (${\ensuremath{\epsilon}}_{n\mathrm{k}}$-${H}_{\mathrm{k}}$)p. For silicon, we obtain 11.3 for ${\ensuremath{\epsilon}}_{1}$(\ensuremath{\omega}=0), compared to 11.7 for experiment, 13.1 in our LDA calculation, and 8.4 in a naive self-energy corrected theory (i.e., simply modifying the eigenvalues without modifying the momentum operator). For germanium, the corresonding values as 16.5, 15.8, 21.3 and 10.4