  The two-dimensional electron system formed at the interface between the
insulating oxides LaAlO3 and SrTiO3 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
LaAlO3 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.
