Spatial Charge Distribution in the LaAlO$_3$-SrTiO$_3$ Interface Measured by Angle Resolved Soft X-ray Absorption

At the interface between complex insulating oxides, novel phases with interesting properties occur. In particular, studies have recently shown high-mobility two-dimensional conducting planes emerge at the interface between insulating oxide heterostructures of LaAlO$_3$ and SrTiO$_3$. Although this state has been predicted and reported to be confined at the interface, transport studies alone cannot measure the charge distribution since mobility may also vary spatially. A way to measure the charge distribution independent of mobility is needed. Here, we present for the first time a direct mapping of the spatial charge density distribution of this system through oxygen vacancy mapping about the interface between LaAlO$_3$/SrTiO$_3$ layers prepared at various oxygen deposition partial pressures using angle resolved soft x-ray absorption. We find that, depending on specific growth protocols, the spatial extension of the oxygen vacancies (charges) can be varied from a 3d-like to a 2d-like distribution at the LaAlO$_3$/SrTiO$_3$ interface.