X-ray Absorption and Resonant X-ray Emission at the Carbon Edge of Li$_2$CO$_3$

Abstract

While highly successful, density functional theory is known to have limitations owing to its neglect of many-body electron-electron interactions. This neglect leads to errors in the single-particle energies, leading to underestimated band gaps and band widths as well as errors in band alignment at interfaces. Many-body perturbation theory, in the form of the $GW$ self-energy correction, has been widely used to improve upon these short-comings. Though less well studied, the same $GW$ method is also able to predict the finite quasiparticle lifetime that is seen to cause anomalous broadening in the lowest-lying lines of valence emission spectra. Using near-edge x-ray absorption and emission, we probe the electronic structure of Li$_2$CO$_3$. Our measurements are compared to first-principles calculations, including $GW$ self-energy corrections to the single-particle energies and excitonic effects from the Bethe-Salpeter equation.