The rich phase diagram of the two dimensional electron gas (2DEG) at the STO/LAO interface is probed using Hall and longitudinal resistivity. Thanks to a special bridge design we are able to tune through the superconducting transition temperature T$_c$ and to mute superconductivity by either adding or removing carriers in a gate bias range of a few volts. Hall signal measurements pinpoint the onset of population of a second mobile band right at the carrier concentration where maximum superconducting T$_c$ and critical field H$_c$ occur. These results emphasize the advantages of our design, which can be applied to many other two dimensional systems assembled on top of a dielectric substrate with high permittivity.
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