Abstract: <p>Experiments have observed a two-dimensional electron gas at the interface of two insulating oxides: strontium titanate (SrTiO<sub>3</sub>) and lanthanum aluminate (LaAlO<sub>3</sub>). These interfaces exhibit metallic, superconducting, and magnetic behaviours, which are strongly affected by impurities. Motivated by experiments, we introduce a simple model in which… more