Two-dimensional electron gasat the interface between two polar oxide materials

Following the discovery of a two-dimensional electron gas (2DEG) at the interface between polar LaAlO$_{3}$ (LAO) and non-polar SrTiO$_{3}$ (STO) grown in the [001] direction many related heterostructures with interesting physical phenomena have been proposed and explored. Here using the first-principles theory, we investigate the electronic band structure of the interface between two polar oxide materials -- a wide materials group that can broaden the field for designing conducing interfaces with novel properties. As a model system, we consider a LAO/STO heterostructure stacking in the [111] direction. In this direction both free standing LAO and STO are polar with alternatively charged planes -- (LaO$_{3})^{3-}$ and Al$^{3+}$ in LAO and (SrO$_{3})^{4-}$ and Ti$^{4+}$ in STO leading to inevitable interface reconstruction. Simple electrostatic arguments suggest that at the Ti/LaO$_{3}$ terminated interface of the LAO/STO(111) heterostructure this reconstruction may be achieved through depositing electron surface charge of 0.5e/$\surd $3a$^{2}$ at the interface. This is by a factor of $\surd $3 smaller than that for the LaO/STO(001) interface which is expected to lead to a larger critical thickness of LAO(111) compared to LAO(001). These arguments are consistent with our first-principles calculations which predict a critical thickness of LAO(111) to be eight (LaO$_{3}$-Al) bilayers. Our findings are consistent with the experimental studies performed by S. Ryu, C. W. Bark, T. Hernandez, M. S. Rzchowski, H. Zhou, D. D. Fong, and C.-B. Eom.