Interplay of excitonic effects and van Hove singularities in optical spectra: CaO and AlN polymorphs

The quasiparticle band structures and fundamental energy gaps of the rock-salt (rs), zinc-blende (zb), and wurtzite (wz) polymorphs of CaO and AlN are calculated within the G₀W₀ approximation on top of a self-consistent solution of the generalized Kohn-Sham equation with the hybrid functional HSE03. Based on these reliable electronic structures, the dielectric functions of rs-CaO, zb-AlN, and wz-AlN including excitonic effects are obtained from the solution of the Bethe-Salpeter equation. The peaks and structures in the absorption spectra are analyzed in terms of critical points in the joint band structure and the joint density of states. We find that some features of the optical absorption can be clearly assigned to bound excitonic states located at M₀ or M₁ critical points, while others are merely due to a large joint density of states.