Imaging Electron Interferometer

Abstract

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)

Unexpected features of branched flow through high-mobility two-dimensional electron gases

“…2, and as detailed in previous work 10,15,25,27 , our imaging technique yields fringes due to the interference of two sets of paths-path 1 (blue), the roundtrip path electrons take from the QPC to the tip and back, and paths 2 (red), the sum of all roundtrip paths electrons take from the QPC to all fixed scatterers in the sample and back. When we move the tip away from the QPC by half the Fermi wavelength, λ F /2, the phases of paths 2 do not change, but the phase accumulated along path 1 increases by 2π; thus, we expect a fringe spacing of λ F /2.…”

“…2, we discover an almost complete absence of hard-scattering from impurities and defects in the highest-mobility material by comparing interference fringes which decorate images of flow in the three samples. All previous sufficiently high-resolution images of electron flow through QPCs using this backscat-4 tering imaging technique have shown interference fringes [9][10][11][12][13][14][15] . However, as shown in Fig.…”

“…1d. Using a recently established technique [9][10][11][12][13][14][15] , we measure the conductance across the QPC while scanning a sharp conducting tip ∼20 nm above the surface of the sample. We negatively bias the tip to create a depletion region in the 2DEG below.…”

“…We also observe two unanticipated phenomena in high-mobility samples. In our highest-mobility sample we observe an almost complete absence of sharp impurity or defect scattering, indicated by the complete suppression of quantum coherent interference fringes.Also, branched flow through the chaotic potential of a high-mobility sample remains stable to significant changes to the initial conditions of injected electrons.Scanning gate microscopy (SGM) images of electron flow in two-dimensional electron gases (2DEGs) [8][9][10][11][12][13][14][15][16][17][18] provide direct spatial information not available in conventional electrical transport measurements. Our SGM studies show how varying disorder affects electron flow, and enable us to infer information about the disorder potential in our different samples.…”

Imaging magnetic focusing of coherent electron waves

“…[18][19][20][21]27 The most basic question for open systems is: "What is the pattern of flow for electron waves?" Imaging flow is difficult, because the electrons are often buried inside a heterostructure, and because low temperatures and strong magnetic fields are needed to observe quantum phenomena.…”