  We report on resistivity and Hall measurements performed on a series of
narrow mesa devices fabricated from LaAlO_3/SrTiO_3 single interface
heterostructure with a bridge width range of 1.5-10 microns. Upon applying
back-gate voltage of the order of a few Volts, a strong increase in the sample
resistance (up to factor of 35) is observed, suggesting a relatively large
capacitance between the Hall-bar and the gate. The high value of this
capacitance is due to the device geometry, and can be explained within an
electrostatic model using the Thomas Fermi approximation. The Hall coefficient
is sometimes a non-monotonic function of the gate voltage. This behavior is
inconsistent with a single conduction band model. We show that a theoretical
two-band model is consistent with this transport behavior, and indicates a
metal to insulator transition in at least one of these bands.
