Effects of electron-phonon coupling on absorption spectrum: <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>K</mml:mi></mml:math> edge of hexagonal boron nitride

A detailed analysis of the theoretical x-ray absorption near-edge structures (XANES) for the boron and nitrogen $K$ edge in hexagonal boron nitride ($h$-BN) employing density-functional theory calculations is presented. The supercell core-hole method and the Bethe-Salpeter equation are used for the description of electron-hole interactions. The calculations are carried out with two different codes, the vasp and the wien2k codes, employing the projector augmented-wave and the full-potential linear augmented-plane-wave methods, respectively. We find close agreement between spectra obtained from the two codes and between calculations using the supercell core-hole method and the Bethe-Salpeter approach. All our calculations, as well as previous calculations using the ground-state structure, yield a single $2{p}_{{\ensuremath{\sigma}}^{*}}$ peak in the boron $K$-edge spectrum and hence fail to describe the experimental double-peak structure. We find that the inclusion of electron-phonon interactions is crucial to obtain the experimentally observed double-peak structure. We include these effects fully parameter free and ab initio using a one-shot sampling method and obtain excellent agreement with experiment.