Coulomb Catastrophe and the Origin of the Sheet Carrier Density at the n-type LaAlO$_3$/SrTiO$_3$ interface: What do band calculations tell us?

Transport measurements of the two-dimensional electron gas (2DEG) at the intrinsic n-type LaAlO$_3$/SrTiO$_3$ interface have found a density of carriers much lower than expected from the ``Coulomb catastrophe" arguments. From a detail density-functional study, we suggest how this discrepancy may be reconciled. We find that electrons occupy multiple subbands at the interface leading to a rich array of transport properties. Some electrons are confined to a single interfacial layer and susceptible to localization, while others with small masses and extended over several layers are expected to contribute to transport.