Imaging coherent electron wave flow through two-dimensional electron gas nanostructures

This thesis presents the first published spatial images showing coherent electron flow through quantum point contacts (QPCs). The QPCs are defined in a high-mobility two-dimensional electron gas (2DEG) existing in a GaAs/Al .3Ga.7As heterostructure. The images of electron flow were obtained using a new technique in which high-speed, low-noise transport measurements are taken at the same time that a charged atomic force microscope (AFM) tip is scanned or positioned directly above the 2DEG. The AFM tip creates a movable depletion disc in the 2DEG which can backscatter electron waves and hence change the conductance of the QPC (or other nanostructure device) when it is positioned in an area of high electron flow. By raster scanning the AFM tip and simultaneously monitoring the conductance of the device, an image of electron flow can be compiled.; The first series of measurements examines the angular current patterns for electron flow through the lowest transverse modes of a QPC. Very good agreement between theory and experiment is found---the number of lobes in the electron flow patterns are found to be equal to the mode number. Coherent interference fringes spaced by half the Fermi wavelength, lambdaF, decorate the images of flow and can be blurred out by using high drain-source bias voltages, leaving behind the envelope of electron flow. The use of the AFM tip as a positionable artificial impurity is also investigated, whereby it can selectively suppress individual conductance plateaus.; A second series of measurements reveals surprising features in electron flow from a quantum point contact at distances greater than about 500nm. The electron flow is found to develop strong branches which split and bend, but which remain narrow throughout the entire scan range. This unexpected feature of the flow has since been investigated theoretically by our collaborators and has been found to be due to the cumulative effects of many small angle scattering events---the branches are related to caustics which form downstream of focussing dips in the potential. Another surprising feature is found in this series of measurements---coherent fringes are found to persist throughout the entire scan range.