Many-body effects in the electronic spectra of cubic boron nitride

We present state of the art first-principles calculations of optical spectra and the loss function of bulk cubic boron nitride $(c\text{\ensuremath{-}}\mathrm{B}\mathrm{N})$, starting from a density functional Kohn-Sham band structure. We investigate the influence of many-body effects beyond the random phase approximation (RPA) on the optical spectra through the inclusion of self-energy and excitonic effects by a GW calculation and the solution of the Bethe-Salpeter equation. For the loss function we only perform RPA calculations, since Bethe-Salpeter results are already available in the literature. We show to which extent, and in which kind of spectra, the description of many-body effects is important for a meaningful comparison with experiment, and when they can be neglected due to mutual cancellation. We also present results obtained within time-dependent density functional theory, both in the adiabatic local density approximation (TDLDA) and using a recently proposed long-range approximation for the exchange-correlation kernel. Our results show that the latter corrects a big part of the error with respect to RPA or TDLDA; however, the corrections are not sufficient to qualify the method for further quantitative predictions, in particular for the study of the optical gap. In fact, since experiments often quote a relatively low (around $6.4\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$) band gap, whereas the calculated optical absorption spectrum already in the random-phase approximation appears blueshifted by more than $2\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ with respect to the available experimental curve, we study in particular the question of the optical gap in this material. It turns out that, although there is evidence for a weakly bound exciton in $c\text{\ensuremath{-}}\mathrm{B}\mathrm{N}$, the optical gap of pure monocrystalline cubic BN should be around $11\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$, hence significantly bigger than has sometimes been quoted from experiments.