Band offsets between SrTiO$_3$ and LaAlO$_3$

Although separately SrTiO$_3$ and LaAlO$_3$ are both band insulators, together a highly mobile, quasi-2D electron gas can form at their interface. Several mechanisms have been proposed to produce this electron gas, including the electrostatic divergence within LaAlO$_3$. A critical property in understanding this divergence is the valence band offset between SrTiO$_3$ and LaAlO$_3$. However, because the electrostatic potential can diverge, it is not clear \emph{where} the valence band offset should be defined; an issue that may affect experimental band offset measurements. In this talk, the band offsets between SrTiO$_3$ and LaAlO$_3$ are presented within the framework of density functional theory. Both the layer projected density of states and macroscopically averaged potential are used to find the valence band offset for thin films and multilayers.