Local Current Distribution and "Hot Spots" in the Integer Quantum Hall Regime

In a recent experiment, the local current distribution of a two-dimensional electron gas in the quantum Hall regime was probed by measuring the variation of the conductance due to local gating. The main experimental finding was the existence of "hot spots", i.e. regions with high degree of sensitivity to local gating, whose density increases as one approaches the quantum Hall transition. However, the direct connection between these "hot spots" and regions of high current flow is not clear. Here, based on a recent model for the quantum Hall transition consisting of a mixture of perfect and quantum links, the relation between the "hot spots" and the current distribution in the sample has been investigated. The model reproduces the observed dependence of the number and sizes of "hot spots" on the filling factor. It is further demonstrated that these "hot spots" are not located in regions where most of the current flows, but rather, in places where the currents flow both when injected from the left or from the right. A quantitative measure, the harmonic mean of these currents is introduced and correlates very well with the "hot spots" positions

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

GaAs-based two-dimensional electron gases (2DEGs) show a wealth of remarkable electronic states, and serve as the basis for fast transistors, research on electrons in nanostructures, and prototypes of quantum-computing schemes. All these uses depend on the extremely low levels of disorder in GaAs 2DEGs, with low-temperature mean free paths ranging from microns to hundreds of microns. Here we study how disorder affects the spatial structure of electron transport by imaging electron flow in three different GaAs/AlGaAs 2DEGs, whose mobilities range over an order of magnitude. As expected, electrons flow along narrow branches that we find remain straight over a distance roughly proportional to the mean free path. 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.Comment: 22 pages, 4 figures, 1 tabl

Spatially resolved manipulation of single electrons in quantum dots using a scanned probe

The scanning metallic tip of a scanning force microscope was coupled capacitively to electrons confined in a lithographically defined gate-tunable quantum dot at a temperature of 300 mK. Single electrons were made to hop on or off the dot by moving the tip or by changing the tip bias voltage owing to the Coulomb-blockade effect. Spatial images of conductance resonances map the interaction potential between the tip and individual electronic quantum dot states. Under certain conditions this interaction is found to contain a tip-voltage induced and a tip-voltage independent contribution.Comment: 4 pages, 4 figure

Intersubband Electron Interaction in 1D-2D Junctions

We have shown that the electron transport through junctions of one-dimensional and two-dimensional systems, as well as through quantum point contacts, is considerably affected by the interaction of electrons of different subbands. The interaction mechanism is caused by Friedel oscillations, which are produced by electrons of the closed subbands even in smooth junctions. Because of the interaction with these oscillations, electrons of the open subbands experience a backscattering. The electron reflection coefficient, which describes the backscattering, has a sharp peak at the energy equal to the Fermi energy and may be as high as about 0.1. This result allows one to explain a number of available experimental facts.Comment: 5 pages, 3 figure

Electron-beam propagation in a two-dimensional electron gas

A quantum mechanical model based on a Green's function approach has been used to calculate the transmission probability of electrons traversing a two-dimensional electron gas injected and detected via mode-selective quantum point contacts. Two-dimensional scattering potentials, back-scattering, and temperature effects were included in order to compare the calculated results with experimentally observed interference patterns. The results yield detailed information about the distribution, size, and the energetic height of the scattering potentials.Comment: 7 pages, 6 figure

Imaging transverse electron focusing in semiconducting heterostructures with spin-orbit coupling

Transverse electron focusing in two-dimensional electron gases (2DEGs) with strong spin-orbit coupling is revisited. The transverse focusing is related to the transmission between two contacts at the edge of a 2DEG when a perpendicular magnetic field is applied. Scanning probe microscopy imaging techniques can be used to study the electron flow in these systems. Using numerical techniques we simulate the images that could be obtained in such experiments. We show that hybrid edge states can be imaged and that the outgoing flux can be polarized if the microscope tip probe is placed in specific positions.Comment: Contribution to the Book/Proceedings of the PITP Les Houches School on "Quantum Magnetism" held on June, 2006. Final forma

Conductance of a Quantum Point Contact in the presence of a Scanning Probe Microscope Tip

Using the recursive Green's function technique, we study the coherent electron conductance of a quantum point contact in the presence of a scanning probe microscope tip. Images of the coherent fringe inside a quantum point contact for different widths are obtained. It is found that the conductance of a specific channel is reduced while other channels are not affected as long as the tip is located at the positions correspending to that channel. Moreover, the coherent fringe is smoothed out by increasing the temperature or the voltage across the device. Our results are consistent with the experiments reported by Topinka et al.[Science 289, 2323 (2000)].Comment: 5 page