Query: Coherent branched flow in a two-dimensional electron gas

Candidate papers:

abstract: Semiconductor nanostructures based on two dimensional electron gases (2DEGs) could form the basis of future devices for sensing, information processing and quantum computation. Although electron transport in 2DEG nanostructures has been well studied, and many remarkable phenomena have already been discovered (for example, weak localization, quantum chaos, universal conductance fluctuations) fundamental aspects of the electron flow through these structures have so far not been clarified. However, it has recently become possible to image current directly through 2DEG devices using scanning probe microscope techniques. Here, we use such a technique to observe electron flow through a narrow constriction in a 2DEG a quantum point contact. The images show that the electron flow from the point contact forms narrow, branching strands instead of smoothly spreading fans. Our theoretical study of this flow indicates that this branching of current flux is due to focusing of the electron paths by ripples in the background potential. The strands are decorated by interference fringes separated by half the Fermi wavelength, indicating the persistence of quantum mechanical phase coherence in the electron flow. These findings may have important implications for a better understanding of electron transport in 2DEGs and for the design of future nanostructure devices.
author_names: Mark A Topinka

Brian J LeRoy

Robert M Westervelt

Scot E J Shaw

Ragnar Fleischmann

Eric J Heller

Kevin D Maranowski

Arthur C Gossard
title: Coherent branched flow in a two dimensional electron gas
venue: Nature
year: 2001

abstract: Semiconductor nanostructures based on two dimensional electron gases (2DEGs) have the potential to provide new approaches to sensing, information processing, and quantum computation. Much is known about electron transport in 2DEG nanostructures and many remarkable phenomena have been discovered (e.g. weak localization, quantum chaos, universal conductance fluctuations)1,2 yet a fundamental aspect of these devices, namely how electrons move through them, has never been clarified. Important details about the actual pattern of electron flow are not specified by statistical measures such as the mean free path. Scanned probe microscope (SPM) measurements allow spatial investigations of nanostructures, and it has recently become possible to directly image electron flow through 2DEG devices using newly developed SPM techniques3 13. Here we present SPM images of electron flow from a quantum point contact (QPC) which show unexpected dynamical channeling the electron flow forms persistent, narrow, branching channels rather than smoothly spreading fans. Theoretical study of this flow, including electron scattering by impurities and donor atoms, shows that the channels are not due to deep valleys in the potential, but rather are caused by the indirect cumulative effect of small angle scattering. Surprisingly, the channels are decorated by interference fringes well beyond where the simplest thermal averaging arguments suggest they should be found. These findings may have important implications for 2DEG physics and for the design of future nanostructure devices.
title: Coherent Branched Flow in a Two Dimensional Electron Gas
year: 2000

abstract: We find a uniform semiclassical (SC) wave function describing coherent branched flow through a two dimensional electron gas (2DEG) a phenomenon recently discovered by direct imaging of the current using scanned probed microscopy[1, 2] The formation of branches has been explained by classical arguments[2] but the SC simulations necessary to account for the coherence are made difficult by the proliferation of catastrophes in the phase space. In this paper, expansion in terms of "replacement manifolds" is used to find a uniform SC wave function for a cusp singularity. The method is then generalized and applied to calculate uniform wave functions for a quantum map model of coherent flow through a 2DEG. Finally, the quantum map approximation is dropped and the method is shown to work for a continuous time model as well.
author_names: Jiri Vanicek

Eric J Heller
title: C D 3 0 A ug 2 00 2 Uniform semiclassical wave function for coherent 2 D electron flow
year: 2020

abstract: We find a uniform semiclassical (SC) wave function describing coherent branched flow through a two dimensional electron gas (2DEG) a phenomenon recently discovered by direct imaging of the current using scanned probed microscopy [M.A. Topinka, B.J. LeRoy, S.E.J. Shaw, E.J. Heller, R.M. Westervelt, K.D. Maranowski, and A.C. Gossard, Science 289, 2323 (2000) The formation of branches has been explained by classical arguments [M.A. Topinka, B.J. LeRoy, R.M. Westervelt, S.E.J. Shaw, R. Fleischmann, E.J. Heller, K.D. Maranowski, and A.C. Gossard, Nature (London) 410, 183 (2001) but the SC simulations necessary to account for the coherence are made difficult by the proliferation of catastrophes in the phase space. In this paper, expansion in terms of "replacement manifolds" is used to find a uniform SC wave function for a cusp singularity. The method is then generalized and applied to calculate uniform wave functions for a quantum map model of coherent flow through a 2DEG. Finally, the quantum map approximation is dropped and the method is shown to work for a continuous time model as well.
author_names: Jiri Vanicek

Eric J Heller
title: Uniform semiclassical wave function for coherent two dimensional electron flow.
venue: Physical review. E, Statistical, nonlinear, and soft matter physics
year: 2003

abstract: The quantum and classical dynamics in a two dimensional (2D) periodic potential influenced by a constant force is discussed and compared. Classically, the dynamics is chaotic. A branched flow of the particles similar but more structured than the coherent branched flow in a 2D electron gas is observed. In the classical case, the formation of separate decay channels is explained by dynamical trapping. The quantum dynamics closely follows the classical one.
author_names: Markus Gluck

F Keck

Andrey R Kolovsky

H J Korsch
title: Branched classical and quantum flow in two dimensional Wannier Stark systems
year: 2002

abstract: The magnetic focusing of electrons has proven its utility in fundamental studies of electron transport. Here we report the direct imaging of magnetic focusing of electron waves, specifically in a two dimensional electron gas (2DEG) We see the semicircular trajectories of electrons as they bounce along a boundary in the 2DEG, as well as fringes showing the coherent nature of the electron waves. Imaging flow in open systems is made possible by a cooled scanning probe microscope. Remarkable agreement between experiment and theory demonstrates our ability to see these trajectories and to use this system as an interferometer. We image branched electron flow as well as the interference of electron waves. This technique can visualize the motion of electron waves between two points in an open system, providing a straightforward way to study systems that may be useful for quantum information processing and spintronics.
author_names: Katherine E Aidala

Roberta E Parrott

Tobias Kramer

Eric J Heller

Robert M Westervelt

Micah P Hanson

Arthur C Gossard
title: Imaging magnetic focusing of coherent electron waves
year: 2007

abstract: This thesis presents several uniform methods improving the accuracy of semiclassi cal approximations to quantum mechanics when the WKB approximation breaks down due to nonlinear underlying dynamics. In our alternative approach, the complicated Lagrangian manifold supporting a singular WKB wavefunction is replaced by a series of simpler La grangian manifolds, and the singular wavefunction is replaced by a convergent series of well behaved semiclassical wavefunctions. This method is successfully applied to a model of homoclinic tangle, for which the WKB wavefunction has an infinite number of singularities, and to the problem of wave scattering from a corrugated wall. A generalized replacement manifold method is employed to find a uniform wave function describing coherent branched flow through a two dimensional electron gas, a phenomenon recently discovered by direct imaging of the current using scanned probed mi croscopy. While the formation of branches has been explained by classical arguments, the semiclassical simulations necessary to account for the coherence are difficult due to the proliferation of catastrophes in phase space. The problem is solved here by using replacement manifolds with complex momenta. The method is first explained and tested on a single cusp catastrophe and then on a realistic model of the coherent branched flow. Another uniform method is used to evaluate the quantum fidelity (Loschmidt echo) This method, based on the classical perturbation approximation and the Initial Value Representation, is numerically tractable and gives remarkably accurate results. Our method explicitly contains the Fermi Golden Rule and Lyapunov regimes of fidelity decay as well as the " building blocks " of analytical theories of recent literature, and thus permits a direct test of the approximations made by other authors. The thesis ends with a discussion of what remains from the theory of the decay of survival probability and the parametric dependence of the local density of states in one dimensional Hamiltonian and disordered systems. We show that a remarkably accurate uniform approximation captures the physics of both perturbative and non perturbative regimes, though it cannot take into account the strong localization effect.
author_names: Shanmuga Sundaram Devasundaram
title: A Thesis Presented to
year: 2003

abstract: Abstract We measure the energy distribution of electrons passing through a two dimensional electron gas using a scanning probe microscope (SPM) We present direct spatial images of coherent electron wave flow from a quantum point contact formed in a GaAs/AlGaAs two dimensional electron gas using a liquid He cooled SPM. A negative voltage is placed on the tip, which creates a small region of depleted electrons that backscatters electron waves. Oscillating the voltage on the tip and locking into this frequency gives the spatial derivative of electron flow perpendicular to the direction of current flow. We show images of electron flow using this method. By measuring the amount of electrons backscattered as a function of the voltage applied to the tip, the energy distribution of electrons is measured.
author_names: Mark A Topinka

Brian J LeRoy

Robert M Westervelt

Kevin D Maranowski

Arthur C Gossard
title: Imaging coherent electron wave flow in a two dimensional electron gas
year: 2002

abstract: Abstract Images of coherent electron flow through a two dimensional electron gas in a GaAs/AlGaAs heterostructure from a quantum point contact (QPC) were obtained at liquid He temperatures by using a scanning probe microscope with a charged tip that backscatters electrons. Near the QPC, at distances less than 500 nm the images show angular lobes of electron flow in patterns determined by the quantum modes of the QPC. At greater distances, narrow branches of electron flow are observed, formed by the cumulative effects of small angle scattering. In addition, the images show fringes spaced by half the Fermi wavelength, evidence that the electron flow is coherent. These observations agree well with theoretical simulations of electron flow.
author_names: Brian J LeRoy
title: Imaging coherent electron flow in a two dimensional electron gas
year: 2003

abstract: We measure the energy distribution of electrons passing through a two dimensional electron gas using a scanning probe microscope. We present direct spatial images of coherent electron wave flow from a quantum point contact formed in a GaAs/AlGaAs two dimensional electron gas using a liquid He cooled SPM. A negative voltage is placed on the tip, which creates a small region of depleted electrons that backscatters electron waves. Oscillating the voltage on the tip and locking into this frequency gives the spatial derivative of electron flow perpendicular to the direction of current flow. We show images of electron flow using this method. By measuring the amount of electrons backscattered as a function of the voltage applied to the tip, the energy distribution of electrons is measured.
author_names: Brian J LeRoy

Ania C Bleszynski

Mark A Topinka

Robert M Westervelt

Scot E J Shaw

Eric J Heller

Kevin D Maranowski

Arthur C Gossard
title: Imaging coherent electron wave flow in a two dimensional electron gas
year: 2003