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Atomic signatures of local environment from core-level spectroscopy in $β$-Ga$_2$O$_3$

We present a joint theoretical and experimental study on core-level excitations from the oxygen $K$ edge of $β$-Ga$_2$O$_3$. A detailed analysis of the electronic structure reveals the importance of O-Ga hybridization effects in the conduction region. The spectrum from O 1$s$ core electrons is dominated by excitonic effects, which overall redshift the absorption onset by 0.5 eV, and significantly redistribute the intensity to lower energies. Analysis of the spectra obtained within many-body perturbation theory reveals atomic fingerprints of the inequivalent O atoms. From the comparison of energy-loss near-edge fine-structure (ELNES) spectra computed with respect to different crystal planes, with measurements recorded under the corresponding diffraction conditions, we show how the spectral contributions of specific O atoms can be enhanced while quenching others. These results suggest ELNES, combined with ab initio many-body theory, as a very powerful technique to characterize complex systems, with sensitivity to individual atomic species and to their local environment.