Signatures of short-range many-body effects in the dielectric function of silicon for finite momentum transfer

We present an investigation of the dynamic structure factor and of the dielectric function εM(Q,ω) of the prototypical semiconductor silicon for finite momentum transfer, combining inelastic x-ray scattering experiments and ab initio calculations. In contrast with optical spectra, for finite momentum transfer time-dependent density-functional theory in the adiabatic local-density approximation together with lifetime broadening describes the physics of valence excitations correctly. Major structures in the spectra, governed by short-range crystal and exchange-correlation local-field effects, are strongly influenced by a mixing of transitions of positive and negative energies, in striking difference to spectra for vanishing momentum transfer. This mixing gives rise to a pronounced Fano asymmetry.