Theory of the Switchable Interfacial Metal-Insulator Transition in LaAlO$_3$ thin films on SrTiO$_3$

Although bulk LaAlO$_3$ and SrTiO$_3$ are both insulating, an electron gas can form at the interface between these compounds. For up to 2 unit cells (uc) of LaAlO$_3$, the interface remains insulating, while for 4 uc and beyond, it is metallic. For 3 uc films, the interface can be reversibly switched from metallic to insulating using voltages applied by an atomic force microscope (AFM). We present first- principles density functional calculations of LaAlO$_3$ films on SrTiO$_3$. We show the AFM induced interfacial metal- insulator transition can be explained by the formation and annihilation of oxygen vacancies on the LaAlO$_3$ surface.