Scanned probe microscopy of the electronic properties of low-dimensional systems

The local electronic properties of low-dimensional systems are explored using a low-temperature atomic force microscope (AFM) sensitive to electrostatic forces. Two low-dimensional systems are measured: a two-dimensional electron gas in the quantum Hall regime, and a one-dimensional electron gas in single-walled carbon nanotubes.; The properties of the edge of a quantum Hall conductor are investigated by studying non-equilibrium edge state populations. Electrostatic force microscopy (EFM) is used to measure the local Hall voltage distribution at the edge of a quantum Hall conductor in the presence of a gate-induced non-equilibrium edge state population. Disequilibrated edge state potentials are clearly observed, with a sharp voltage drop seen near the edge of the sample. Equilibration of the edge state potentials by inter edge state scattering is also imaged locally with EFM. Scanned gate microscopy (SGM) is used to probe the inter edge state scattering further, by investigating the scattering mechanisms involved. Scattering is found to be dominated by individual scattering centers, which are imaged with SGM. Evidence is found for scattering from both weak links between the edge states and microscopic impurities.; The local electronic properties of carbon nanotubes are explored by studying single-electron charging effects in quantum dots that form within the nanotubes. SGM is used to locate individual quantum dots in a nanotube and observe Coulomb oscillations in their conductance. The dependence of the scanned gate images on the AFM tip voltage is found to be influenced strongly by the electrostatic environment of the nanotube, and a phenomenological model is introduced to describe these effects. EFM measurements are used to detect Coulomb oscillations in the electrostatic force exerted by the nanotube on the AFM tip. These Coulomb oscillations in the force are due to the change in the electrostatic potential of the quantum dot associated with single electron charging. Coulomb oscillations in the resonant frequency of the AFM cantilever are also observed, due to the spatial gradient of the force exerted by the dot. In both cases, quantitative agreement with theory is obtained. Finally, degradation of the Q -factor of the cantilever resonance is observed at the same locations as the Coulomb oscillations in the conductance, the force, and the resonance frequency. An explanation in terms of dissipation of the cantilever energy through coupling to single electron motion in the quantum dot is proposed.