  Nanoscale control of the quasi-two-dimensional electron gas at the
LaAlO3/SrTiO3 (LAO/STO) interface by a conductive probe tip has triggered the
development of a number of electronic devices. While the spatial distribution
of the conductance is crucial for such devices, it is challenging to directly
visualize the local electrical properties at the buried interface. Here we
demonstrate conductivity imaging of sketched nanostructures at the LAO/STO
interface by microwave impedance microscopy (MIM) with a lateral resolution on
the order of 100 nm. The sheet conductance extracted from the MIM data agrees
with the transport measurement. The tip-induced insulator-to-metal transition
is observed above a threshold voltage of +4 V. Our work paves the way to study
emergent phenomena at oxide interfaces by probing nanoscale conductance
distribution.
