Quasiparticle calculation of the dielectric response of silicon and germanium

We calculate the dielectric function ε₁({ω}) of silicon and germanium for frequencies below the direct band gap at the experimental lattice constant as well as the pressure dependence of the static dielectric constant ε₁(P). Our theory is an extension of the local-density approximation (LDA). We include self-energy effects by adding an operator to the usual LDA Hamiltonian; i.e., Hₖ=HₖLDA+Δₖ{P}ck. This form leads to a Ward-identity replacement p→({{{ε}}}ₙₖ$-${H}ₖLDA)^-1(εₙₖ -Hₖ)p. Our theory is in agreement with experiment for ε₁({ω}) at the level of a few percent. For ε₁(P), we are in agreement with experiments for silicon and some of the conflicting experiments for germanium. A prediction is made for the pressure dependence of the dielectric function of silicon beyond the linear regime.