  LaAlO3/SrTiO3 heterostructures are known to exhibit a sharp, hysteretic
metal-insulator transition (MIT) with large enhanced capacitance near
depletion. To understand the physical origin of this behavior, the
electromechanical response of top-gated LaAlO3/SrTiO3 heterostructures is
probed using two simultaneous measurement techniques: piezoforce microscopy
(PFM) and capacitance spectroscopy. PFM measurements reveal local variations in
the hysteretic response, which is directly correlated with capacitance
measurements. The enhanced capacitance at the MIT is linked to
charging/discharging dynamics of nanoscale conducting islands, which are
revealed through PFM imaging and time-resolved capacitance and piezoresponse
measurements.
