Images of electron flow from the quantum point contact (QPC) are obtained by raster scanning a negatively charged SPM tip above the surface of the device and simultaneously measuring the position-dependent conductance of the device. The negatively charged tip capacitively couples to the 2DEG, creating a depletion region that backscatters electron waves. When the tip is positioned over areas with high electron flow from the QPC the conductance is decreased, whereas when the tip is over areas of relatively low electron flow the conductance is unmodified. By raster scanning the tip over the sample and simultaneously recording the effect the tip has on device conductance, a two dimensional image of electron flow can be obtained.The quantum point contact sample is mounted in an atomic force microscope and cooled to liquid He temperatures. The QPC is formed in the 2DEG inside a GaAs/AlGaAs heterostructure by negatively biasing two gates on the surface -a negative potential on these gates creates two depletion regions that define a variable width channel between them as shown in Fig. 1a. The conductance of the QPC is measured using an ac lock-in amplifier at 11kHz. The heterostructure for the devices used in this experiment was grown by molecular beam epitaxy on an n-type GaAs substrate.The 2DEG resides 57 nm below the surface with mobility µ = 1.0x10 6 cm 2 /Vs and density n = 4.5x10 11 /cm 2 . These values of mobility and density correspond to a mean free path l = 11 µm, Fermi wavelength λ F = 37 nm, and Fermi energy E F = 16 meV. The root mean square voltage across the QPC was chosen so as to not heat electrons -0.2 mV for 1.7K scans. The conductance of the quantum point contact, shown in Fig. 1b, increases as the width of the channel is increased (by changing the gate voltage V g ) and shows well defined conductance plateaus at integer multiples of the conductance quantum 2e 2 /h 1,2 . When probing the electron flow, the SPM tip was held at a negative potential relative to the 2DEG and was scanned at 10nm above the surface of the heterostructure. Figures 2a and 2b show images of electron flow from two different quantum point contacts at the temperature 1.7K; both QPCs are biased on the G = 2e 2 /h conductance plateau. Figure 2b shows the flow patterns on each side of a quantum point contact (the gated region at the center was not scanned), and Figure 2a shows a higher-resolution image of flow from one side of a different QPC.In both these images, the current exits the point contact in a central lobe, as would be expected from an exact quantum-mechanical calculation of electron flow through an ideal QPC without impurities or non-uniform distributions of dopant atoms. Rather than continuing out as a smoothly widening fan, it quickly forks into several different paths and continues to branch off into ever smaller rivulets for the full width of the scan. This branching behavior was observed in all of the 13 QPC exit patterns observed so far. Previously, there have been suggestions of an unexpected narrowness in observe...

Scanning a charged tip above the two-dimensional electron gas inside a gallium arsenide/aluminum gallium arsenide nanostructure allows the coherent electron flow from the lowest quantized modes of a quantum point contact at liquid helium temperatures to be imaged. As the width of the quantum point contact is increased, its electrical conductance increases in quantized steps of 2 e(2)/h, where e is the electron charge and h is Planck's constant. The angular dependence of the electron flow on each step agrees with theory, and fringes separated by half the electron wavelength are observed. Placing the tip so that it interrupts the flow from particular modes of the quantum point contact causes a reduction in the conductance of those particular conduction channels below 2 e(2)/h without affecting other channels.

The public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggesstions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA, 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any oenalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. a. REPORT 1-Aug-2004 Standard Form 298 (Rev 8/98) ABSTRACT The research supported by this grant is aimed at imaging the flow of electron waves through a two dimensional electron gas (2DEG) to understand both the fundamental quantum behavior that appears in semiconductor nanostructures at low temperatures, and to study the propagation of electron waves through semiconductor structures with interesting geometries. A custom-made liquid He cooled scanning probe microscope (SPM) was developed in Westervelt's group to carry out the measurements. The conducting SPM tip acts as a moveable gate that locally depletes the electron gas below, creating a scattering center that reflects electron waves. By measureing the conductance of the devices as the SPM tip is raster scanned above, an image of electron flow is obtained. Electron flow was imaged in two types of devices: (1) An Electron Interferometer, in which electron waves traveling away from a quantum point contact (QPC) reflect both from a mirror and from the depleted disc beneath the SPM tip. (2) Magnetic Focusing device, in which electrons traveling away from a QPC flow around cyclotron orbits in a perpendicular magnetic field and leave through a second QPC pointed in the same direction-a peak in conductance is observed when the spacing between the two QPCs is an integer multiple of the cyclotron diameter. (a) Papers published in peer-reviewed journals (N/A for none)

Recent experimental work in the Westervelt laboratory at Harvard has succeeded in directly imaging electron flow in two degree of freedom electron gasses formed in semiconductor microstructures. Here, we give a brief account of the unexpected high resolution of the resulting images, the surprising branching of the flow which was observed, and the survival of quantum fringing beyond where it was thought to have been obliterated by thermal effects.

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