Pseudopotential Bethe-Salpeter calculations for shallow-core x-ray absorption near-edge structures: excitonic effects in Al2O3

We present an ab initio description of optical and shallow-core x-ray absorption spectroscopies in a unified formalism based on the pseudopotential plane-wave method at the level of the Bethe-Salpeter equation (BSE) within Green's functions theory. We show that norm-conserving pseudopotentials are reliable and accurate not only for valence, but also for semicore electron excitations. In order to validate our approach, we compare BSE absorption spectra obtained with two different codes: the pseudopotential-based code EXC and the all-electron full-potential code Exciting. We take corundum $α$-Al$_2$O$_3$ as an example, being a prototypical material that presents strong electron-hole interactions for both valence and core electron excitations. We analyze in detail the optical absorption spectrum as well as the Al L$_1$ and L$_{2,3}$ edges in terms of anisotropy, crystal local fields, interference and excitonic effects. We perform a thorough inspection of the origin and localization of the lowest-energy excitons, and conclude highlighting the purely electronic character off the pre-edge of L$_1$ and the dichroic nature of the optical and L$_{23}$ spectra.