Ab initio calculations of absorption spectra of semiconducting nanowires within many-body perturbation theory

We present a study of the optical absorption spectra of thin silicon nanowires using many-body perturbation theory. We solve the Bethe-Salpeter equation in the static approximation using a technique that avoids explicit calculation of empty electronic states, as well as storage and inversion of the dielectric matrix. We provide a detailed assessment of the numerical accuracy of this technique, when using plane wave basis sets and periodically repeated supercells. Our calculations show that establishing numerical error bars of computed spectra is critical, in order to draw meaningful comparisons with experiments and between results obtained within different algorithms. We also discuss the influence of surface structure on the absorption spectra of nanowires with $\ensuremath{\simeq}$1-nm diameter. Finally, we compare our calculations with those obtained within time-dependent density functional theory and find substantial differences, more pronounced than in the case of Si nanoparticles with the same diameter.