Imaging a two-dimensional electron system with a scanning charged probe

We introduce a new and conceptually simple scanning probe method to resolve potential fluctuations within a GaAs two-dimensional electron system (2DES). The method employs a charged metal tip to deplete locally the 2DES. The depletion is detected as a reduction in capacitance, measured using a cryogenic transistor attached directly to the tip. The resulting images exhibit contrast arising from variations in the disorder potential. We find the disorder forms random patterns dominated by length scales greater than 0.5 μm. This surprising result is not consistent with present theories, which predict that no preferred wavelengths should be present on the micron scale.