Topographic Mapping of the Quantum Hall Liquid using a Few-Electron Bubble

A scanning probe technique was used to obtain a high-resolution map of the random electrostatic potential inside the quantum Hall liquid. A sharp metal tip, scanned above a semiconductor surface, sensed charges in an embedded two-dimensional electron gas. Under quantum Hall effect conditions, applying a positive voltage to the tip locally enhanced the 2D electron density and created a ``bubble'' of electrons in an otherwise unoccupied Landau level. As the tip scanned along the sample surface, the bubble followed underneath. The tip sensed the motions of single electrons entering or leaving the bubble in response to changes in the local 2D electrostatic potential.Comment: 4 pages, 3 JPG figures, Revtex. For additional info and AVI movies, visit http://electron.mit.edu/st

A New Class of Resonances at the Edge of the Two Dimensional Electron Gas

We measure the frequency dependent capacitance of a gate covering the edge and part of a two-dimensional electron gas in the quantum Hall regime. In applying a positive gate bias, we create a metallic puddle under the gate surrounded by an insulating region. Charging of the puddle occurs via electron tunneling from a metallic edge channel. Analysis of the data allows direct extraction of this tunneling conductance. Novel conductance resonances appear as a function of gate bias. Samples with gates ranging from 1-170~$\mu$m along the edge display strikingly similar resonance spectra. The data suggest the existence of unexpected structure, homogeneous over long length scales, at the sample edge.Comment: 13 pages (revtex) including 4 figure

Imaging Transport Resonances in the Quantum Hall Effect

We use a scanning capacitance probe to image transport in the quantum Hall system. Applying a DC bias voltage to the tip induces a ring-shaped incompressible strip (IS) in the 2D electron system (2DES) that moves with the tip. At certain tip positions, short-range disorder in the 2DES creates a quantum dot island in the IS. These islands enable resonant tunneling across the IS, enhancing its conductance by more than four orders of magnitude. The images provide a quantitative measure of disorder and suggest resonant tunneling as the primary mechanism for transport across ISs.Comment: 4 pages, 4 figures, submitted to PRL. For movies and additional infomation, see http://electron.mit.edu/scanning/; Added scale bars to images, revised discussion of figure 3, other minor change

Quantum orientational melting of mesoscopic clusters

By path integral Monte Carlo simulations we study the phase diagram of two - dimensional mesoscopic clusters formed by electrons in a semiconductor quantum dot or by indirect magnetoexcitons in double quantum dots. At zero (or sufficiently small) temperature, as quantum fluctuations of particles increase, two types of quantum disordering phenomena take place: first, at small values of quantum de Boer parameter q < 0.01 one can observe a transition from a completely ordered state to that in which different shells of the cluster, being internally ordered, are orientationally disordered relative to each other. At much greater strengths of quantum fluctuations, at q=0.1, the transition to a disordered (superfluid for the boson system) state takes place.Comment: 4 pages, 6 Postscript figure