  Novel electronic systems forming at oxide interfaces comprise a class of new
materials with a wide array of potential applications. A high mobility electron
system forms at the LaAlO$_3$/SrTiO$_3$ interface and, strikingly, both
superconducts and displays indications of hysteretic magnetoresistance. An
essential step for device applications is establishing the ability to vary the
electronic conductivity of the electron system by means of a gate. We have
fabricated metallic top gates above a conductive interface to vary the electron
density at the interface. By monitoring capacitance and electric field
penetration, we are able to tune the charge carrier density and establish that
we can completely deplete the metallic interface with small voltages. Moreover,
at low carrier densities, the capacitance is significantly enhanced beyond the
geometric capacitance for the structure. In the same low density region, the
metallic interface overscreens an external electric field. We attribute these
observations to a negative compressibility of the electronic system at the
interface. Similar phenomena have been observed previously in semiconducting
two-dimensional electronic systems. The observed compressibility result is
consistent with the interface containing a system of mobile electrons in two
dimensions.
