A Universal Critical Density Underlying the Physics of Electrons at the LaAlO$_{3}$/SrTiO$_{3}$ Interface

The two-dimensional electron system formed at the interface between the insulating oxides LaAlO$_{3}$ and SrTiO$_{3}$ exhibits ferromagnetism, superconductivity, and a wide range of unique magnetotransport properties. A key challenge is to find a unified microscopic mechanism that underlies these emergent phenomena. Here we show that a universal Lifshitz transition between d-orbitals lies at the core of the observed transport phenomena in this system. Our measurements find a critical electronic density at which the transport switches from single to multiple carriers. This density has a universal value, independent of the LaAlO$_{3}$ thickness and electron mobility. The characteristics of the transition, its universality, and its compatibility with spectroscopic measurements establish it as a transition between d-orbitals of different symmetries. A simple band model, allowing for spin-orbit coupling at the atomic level, connects the observed universal transition to a range of reported magnetotransport properties. Interestingly, we also find that the maximum of the superconducting transition temperature occurs at the same critical transition, indicating a possible connection between the two phenomena. Our observations demonstrate that orbital degeneracies play an important role in the fascinating behavior observed so far in these oxides. Ref: arxiv.org/abs/1110.2184