First-principles predictions of perovskite-type alkali metal titanium oxyhydrides with two-dimensional electronic states

The electric properties of perovskite-type oxides $AB\mathrm{O}_3$ can be controlled by substituting $A$ and $B$ cations, while their chemical compositions are limited by the charge neutrality, e.g., $A^{2+}B^{4+}\mathrm{O}^{2-}_3$. A way of realizing other compositions is substitution of oxygen atoms with monovalent anions, e.g., $A^+B^{4+}\mathrm{O}^{2-}_2X^-$. Such substitution has been recently realized in experiments with fluorine atoms\footnote{T. Katsumata et al., J. Appl. Phys. 104, 044101 (2008).}, and more recently, with hydrogen\footnote{Y. Kobayashi \textit{et al}., Nature Mater. \textbf{11}, 507 (2012)}. Since the valence orbital character of hydrogen atoms ($s$) is different from that of oxygen and fluorine atoms ($p$), oxyhydrides should exhibit interesting electronic properties. In this study, we explore the property of unsynthesized oxyhydrides $A\mathrm{TiO}_2\mathrm{H}$ for alkali metals $A$ by first-principles calculations\footnote{For $A = \mathrm{K}$, N. Sato and S. Tsuneyuki, Appl. Phys. Lett. \textbf{109}, 172903 (2016).}. For $A = \mathrm{K}$, $\mathrm{Rb}$, $\mathrm{Cs}$, two-dimensional electronic states emerge at the valence band maximum, which has $\mathrm{H}$ $1s$ characteristics. Their dielectric and piezoelectric properties are also discussed.