Excitations in cubic BaSnO$_{3}$: a consistent picture revealed by combining theory and experiment

Among the transparent conducting oxides, the perovskite barium stannate is the most promising candidate for various electronic applications due to its outstanding carrier mobility achieved at room temperature. Experimental reports on its characteristics, in terms of its band gap, effective masses, and absorption edge are quite controversial. Here, we provide a fully consistent picture by combining state-of-the-art $ab~initio$ methodology with forefront electron energy-loss spectroscopy (EELS) and optical absorption measurements. EELS data obtained from microscopic, clean, and defect-free sample regions of a BaSnO$_{3}$ single crystal, allow us to determine the properties of the perfect crystal. By temperature-dependent optical absorption measurements, we assess band gap renormalization effects induced by electron-phonon coupling. Our high-resolution EELS measurements are able to capture also very weak excitations below the optical gap, attributed to indirect transitions. Overall, we find for the effective electronic mass, the direct and the indirect gap, the optical gap as well as the absorption onsets and spectra excellent agreement between both experimental techniques and the theoretical many-body results. The latter reveal a medium-scale electron-hole attraction of the lowest bound excitons. Furthermore, our combined investigation supports the picture of a phonon-mediated mechanism where indirect transitions are activated by phonon-induced symmetry lowering, as proposed in a recent theoretical study.