Electrical probes of mesoscopic systems with a low temperature atomic force microscope

We have developed a low temperature atomic force microscope (AFM) for studying transport in mesoscopic systems. Unlike previous methods for measuring these systems, the AFM is a relatively non-invasive probe with high spatial resolution. It has been used to introduce a local scattering site into a mesoscopic constriction and to measure the voltage distribution in Quantum Hall conductors.;To develop the low temperature AFM, we modified conventional AFM designs. In particular, our microscope includes a walker system and a piezoresistive cantilever. The walker provides coarse translation capability for the sample in all three directions and is functional over the entire temperature range. The piezoresistive cantilever detects forces on the AFM tip and is easy to use in the low temperature environment.;We scanned the AFM tip over a constriction in a two-dimensional electron gas and demonstrated that the conductance of the constriction can be both enhanced and reduced by the AFM tip depending on its voltage. Furthermore, when the experiment was repeated in the Quantum Hall regime, we were able to infer the magnitude of the local electron density change in the sample produced by the tip.;To determine how the current is distributed in Quantum Hall conductors, we developed a novel technique for using the AFM to measure local voltages. The results reveal that the current distribution in these devices is characterized by three distinct regimes depending, on the magnetic field. On the Quantum Hall plateaus, the current is distributed non-uniformly throughout the bulk of the device. The other two regimes occur in the transition regions between the plateaus. There, the current distribution changes from a uniform disttibution to one concentrated at the edges of the sample with increasing magnetic field. These results are consistent with the current theoretical understanding of Quantum Hall systems when the small, but non-zero, longitudinal conductivity is included.