Ab initio study of Ba$_{\mathrm{1-x}}$Sr$_{\mathrm{x}}$SnO$_{\mathrm{3}}$ and BaSn$_{\mathrm{1-x}}$M$_{\mathrm{x}}$O$_{\mathrm{3}}$ (M $=$ Bi, Pb) using the ACBN0 functional: structural, electronic and optical properties

Using the recently developed pseudo-hybrid Hubbard density functional ACBN0 [1], we have studied the structural, electronic and optical properties of Ba$_{\mathrm{1-x}}$Sr$_{\mathrm{x}}$SnO$_{\mathrm{3}}$ and BaSn$_{\mathrm{1-x}}$M$_{\mathrm{x}}$O$_{\mathrm{3}}$(M $=$ Bi, Pb). This study is motivated by recent experimental results which show that the solid solutions of BaSnO$_{\mathrm{3}}$ mixed with Bi, Sr or Pb remain transparent for a wide range of mixing ratio (up to 40 percent). While traditional DFT calculations on native BaSnO$_{\mathrm{3}}$ and BaBiO$_{\mathrm{3}}$ fail to open the gap (both systems result as semi-metals), thereby hindering the study of related materials, we demonstrate that using ACBN0, the band gaps open and are in good agreement with experiments. Particularly, in BaBiO$_{\mathrm{3}}$, we correctly reproduce the crystal structure instability caused by the well-known breathing and tilting modes of the oxygens, and the alternating ordering of Bi$^{\mathrm{3+\thinspace }}$and Bi$^{\mathrm{5+\thinspace \thinspace }}$ions. A detailed theoretical investigation of the alloyed systems together with some most recent experimental results will be discussed. [1] L.A. Agapito, S. Curtarolo, and M. Buongiorno Nardelli. \textit{Reformulation of DFT}$+$\textit{U as a Pseudohybrid Hubbard Density Functional for Accelerated Materials Discovery, }Phys. Rev. X \textbf{5, }011006 (2015).