Stoichiometry, defects, and the polar catastrophe in LaAlO$_3$ thin films on SrTiO$_3$

Careful growth of LaAlO$_3$ thin films on SrTiO$_3$ by molecular beam epitaxy has shown that the La/Al ratio of the nominal LaAlO$_3$ layer is key to the formation of a two-dimensional electron liquid at the interface---metallic conductivity is only observed in Al-rich films. The interfacial electron liquid forms due to the polar catastrophe, the diverging potential caused by the atomic layer arrangement at the interface when polar LaAlO$_3$ is grown on TiO$_2$-terminated non-polar SrTiO$_3$. The system eventually reconstructs, moving negative charges to the interface to screen the diverging potential. I will present density functional calculations of the defects that form in LaAlO$_3$ on SrTiO$_3$ to accomodate variations in stoichiometry. In La-rich films, the lowest energy defects are extended and allow cation vacancies to move to the interface to screen the diverging potential. Thus the interface between La-rich LaAlO$_3$ and SrTiO$_3$ remains insulating. In Al-rich films, the defects are localized and block cation motion. In this case a conducting electron liquid forms to screen the diverging potential.