  The interface between the two band insulators SrTiO3 and LaAlO3 unexpectedly
has the properties of a two dimensional electron gas. It is even
superconducting with a transition temperature, Tc, that can be tuned using gate
bias Vg, which controls the number of electrons added or removed from the
interface. The gate bias - temperature (Vg, T) phase diagram is characterized
by a dome-shaped region where superconductivity occurs, i.e., Tc has a
non-monotonic dependence on Vg, similar to many unconventional superconductors.
In this communication the frequency of the quantum resistance-oscillations
versus inverse magnetic field is reported for various Vg. This frequency
follows the same nonmonotonic behavior as Tc; similar trend is seen in the low
field limit of the Hall coefficient. We theoretically show that electronic
correlations result in a non-monotonic population of the mobile band, which can
account for the experimental behavior of the normal transport properties and
the superconducting dome.
