Electron interferometer formed with a scanning probe tip and quantum point contact

Abstract

We show an electron interferometer between a quantum point contact (QPC) and a scanning gate microscope (SGM) tip in a two-dimensional electron gas. The QPC and SGM tip act as reflective barriers of a lossy cavity; the conductance through the system thus varies as a function of the distance between the QPC and SGM tip. We characterize how temperature, electron wavelength, cavity length, and reflectivity of the QPC barrier affect the interferometer. We report checkerboard interference patterns near the QPC and, when injecting electrons above or below the Fermi energy, effects of dephasing. PACS numbers: 85.35.Ds, 73.23.Ad When electronic device dimensions become smaller than the electron coherence length, the wavelike nature of electrons becomes critical to understanding device operation and provides opportunities to build devices taking advantage of quantum properties. Interferometers have been used to study electron interference in systems such as carbon nanotubes [1] and GaAs two-dimensional electron gases (2DEGs) [2]. Direct spatial visualizations of interference effects appear as fringes in images of electron flow in 2DEGs taken by scanning gate microscopy (SGM) [3,4] and can give information about the local potential [5,6].Fringes appear in SGM images when different reflected electron paths interfere. Previously observed fringes were due to an interferometer similar to a Michelson interferometer. One path of the interferometer is created by an SGM tip and the other path by impurities [3][4][5] or a reflector gate [7]. However, fringes were not seen in highmobility samples with a low density of impurities [6]. In this Rapid Communication we report interference fringes in SGM images taken in one of the same high-mobility samples at lower temperatures. Now multiple interfering paths are created by the SGM tip, similar to the movable reflector of a Fabry-Pérot interferometer. We report spatial interference patterns different from those previously observed. The recovery of fringes in clean samples at lower temperatures allows us to spatially probe phase coherent properties, such as local phase and electron wavelength, and we demonstrate how these may be useful for studying dephasing. Furthermore, the understanding of interference fringes which we achieve is necessary before using fringes of a different origin to measure electron interactions in nanostructures [8].Thermal averaging limits how far from a coherent source interference effects can be observed, even if each individual electron is still coherent [9]. Electrons around the Fermi energy with a spread in energies comparable to the thermal energy are involved in transport and FIG. 1: Mechanisms for interference fringe formation and appearance of fringes at low temperature. (a) Schematic of imaging technique showing the 2DEG (green), as well as surface gates and metallic tip (orange) creating depletion regions (black) in the 2DEG below. When above an area of high electron flow, the tip scatters electrons back through the QPC (blue path) and reduces the mea...

Scanning-gate-induced effects in nonlinear transport through nanostructures

“…This phase shift could be related with the well-defined phase conditions observed as a function of V in the difference of conductance changes between two tip positions [7]. Interestingly, while the oscillations decay as (k F x) −1 for g (1) 1 , there is no such decay for the leading nonlinear term g (1) 2 , which dominates the conductance correction at large distances.…”

“…The use of a scanning tunneling microscope (STM) to obtain information about the local field was proposed 25 years ago [1,3,6], but only recently [7][8][9][10] a related technique, the scanning gate microscopy (SGM), has been applied in the nonlinear regime to study electron-electron scattering in a two-dimensional electron gas (2DEG) surrounding a quantum point contact (QPC). The SGM appears as a less invasive probe than the STM, as it consists of a charged atomic force microscope scanning over the sample and thus modifying the conductance only through a capacitive coupling to the buried 2DEG [11][12][13].…”

Signatures of spin-orbit coupling in scanning gate conductance images of electron flow from quantum point contacts

“…It stems from the interference between the waves reflected back by the tip and their reflection from the QPC gates. 20 The maps obtained in the presence of SO interaction are displayed in Fig. 3(d-f).…”

“…20 These conductance oscillations appear due to interference between the wave function flowing from the constriction and backscattered from the tip. These oscillations in the experiments 8 are treated as a signature of the coherent transport.…”

“…15,16 Moreover it has been found that the electron current after leaving the QPC propagates in narrow branches 17,18 and that checkerboard interference patterns 19 are observed in the maps of the electron flow. 20 Recent experiments measured nonequilibrium transport phenomena in QPCs 21 and demonstrated the control of the edge channel trajectories in the quantum Hall regime. 22 Recent theoretical studies on SGM in QPC systems delivered a perturbative description 23 of the transport and a temperature-induced amplification of the interference fringes.…”