Electrostatic stability of insulating surfaces: Theory and applications

We analyze the electrostatic stability of insulating surfaces in the framework of the bulk modern theory of polarization. We show that heuristic arguments based on a fully ionic limit find formal justification at the microscopic level, even in solids where the bonding has a mixed ionic and covalent character. Based on these arguments, we propose simple criteria to construct arbitrary nonpolar terminations of a given bulk crystal. We illustrate our ideas by performing model calculations of several LaAlO${}_{3}$ and SrTiO${}_{3}$ surfaces. We find in the case of ideal LaAlO${}_{3}$ surfaces that cleavage along a higher-index $(01n)$ direction is energetically favorable compared to the polar (100) orientation. In the presence of external adsorbates or defects, the picture can change dramatically, as we demonstrate in the case of H${}_{2}$O/LaAlO${}_{3}$(100).