The metallic tip of a scanning force microscope operated at 300 mK is used to locally induce a potential in an fully controllable double quantum dot defined via local anodic oxidation in a GaAs/AlGaAs heterostructure. Using scanning gate techniques we record spatial images of the current through the sample for different numbers of electrons on the quantum dots, i.e. for different quantum states. Owing to the spatial resolution of current maps, we are able to determine the spatial position of the individual quantum dots, and investigate their apparent relative shifts due to the voltage applied to a single gate.

The functionality of nanostructures fabricated via local anodic oxidation is limited by undesired leakage currents. We use low-temperature scanning gate microscopy to pin down the spatial position where leakage currents are most likely to occur. We show that leakage currents do not flow homogeneously along the complete barrier but at distinct weak points such as crossings of two oxide lines. These findings can be used to improve the design of such nanostructures.