Electronic structure and thermodynamic stability of the SrTiO$_3$ (111) surface*

We investigate the electronic structure and thermodynamic stability of the SrTiO$_3$ (111) surface using density functional theory. We observe that, for the Ti-terminated SrTiO$_3$ (111) surface, there is indeed some electronic reconstruction, resulting in the emergence of a metallic surface state. Polar distortions play a crucial role in screening the internal electric field; thereby reducing the amount of charge transferred between the surfaces. Our analysis emphasizes the failure of the simple nominal charge counting argument in thin STO (111) slabs, which ignores the effect of polar distortion. As expected, having a surface oxygen atom at the Ti termination can stabilize the system, eliminating any electronic reconstruction, making the system insulating. An analysis of the surface thermodynamic stability suggests that the Ti terminated (111) surface should be experimentally realizable. This surface may be useful for exploring the behavior of electrons in oxide (111) interfaces and may have implications for modern device applications.