2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/209807Transport measurements of the two-dimensional electron gas (2DEG) at the LaAlO$_3$/SrTiO$_3$ interface have found a density of carriers much lower than expected from the "polar 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.4 pages, 7 figures, Accepted in Phys. Rev. LettMaterials Sciencetext