Phonon-assisted optical absorption in BaSnO$_3$ from first principles

The perovskite BaSnO$_3$ provides a promising platform for the realization of an earth abundant $n$-type transparent conductor. Its optical properties are dominated by a dispersive conduction band of Sn $5s$ states, and by a flatter valence band of O $2p$ states, with an overall indirect gap of about $2.9$ eV. Using first-principles methods, we study the optical properties of BaSnO$_3$ and show that both electron-phonon interactions and exact exchange, included using a hybrid functional, are necessary to obtain a qualitatively correct description of optical absorption in this material. In particular, the electron-phonon interaction drives phonon-assisted optical absorption across the minimum indirect gap and therefore determines the absorption onset, and it also leads to the temperature dependence of the absorption spectrum. Electronic correlations beyond semilocal density functional theory are key to detemine the dynamical stability of the cubic perovskite structure, as well as the correct energies of the conduction bands that dominate absorption. Our work demonstrates that phonon-mediated absorption processes should be included in the design of novel transparent conductor materials.