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Electron dichotomy on the SrTiO$_3$ defect surface augmented by many-body effects

In a common paradigm, the electronic structure of condensed matter is divided into weakly and strongly correlated compounds. While conventional band theory usually works well for the former class, many-body effects are essential for the latter. Materials like the familiar SrTiO$_3$ compound that bridge or even abandon this characterization scheme are highly interesting. Here it is shown by means of combining density functional theory with dynamical-mean field theory that oxygen vacancies on the STO (001) surface give rise to a dichotomy of weakly-correlated $t_{2g}$ low-energy quasiparticles and localized 'in-gap' states of dominant $e_g$ character with subtle correlation signature. We furthermore touch base with recent experimental work and study the surface instability towards magnetic order.