B. L. Johnson

An experimental study of the onset of parametrically pumped surface waves in viscous fluids

We measure the threshold accelerations necessary to excite surface waves in a vertically vibrated fluid container (the Faraday instability). Under the proper conditions, the thresholds and onset wavelengths agree with recent theoretical predictions for a laterally infinite, finite-depth container filled with a viscous fluid. Experimentally, we show that by using a viscous, non-polar fluid, the finite-size effects of sidewalls and the effects of surface contamination can be made negligible. We also show that finite-size corrections are of order h/L , where h is the fluid depth and L the container size. Based on these measurements, one can more easily interpret certain unexpected observations from previous experimental studies of the Faraday instability.

Resonance patterns of an antidot cluster: From classical to quantum ballistics

We explain the experimentally observed Aharonov-Bohm (AB) resonance patterns of an antidot cluster by means of quantum and classical simulations and Feynman path integral theory. We demonstrate that the observed behavior of the AB period signals the crossover from a low B regime which can be understood in terms of electrons following classical orbits to an inherently quantum high B regime where this classical picture and semiclassical theories based on it do not apply.

Composite fermion theory, edge currents and the fractional quantum Hall effect

We present a mean field theory of composite fermion edge channel transport in the fractional and integer quantum Hall regimes. An expression relating the electrochemical potentials of composite fermions at the edges of a sample to those of the corresponding electrons is obtained, and a plausible form is assumed for the composite fermion Landau level energies near the edges. The theory yields the observed fractionally quantized Hall conductances and also explains other experimental results. We also discuss briefly some experiments that are relevant to the question as to whether fractional edge states in real devices should be described as Fermi or Luttinger liquids.

Novel quantum hall phenomena in arrays of quantum dots

Abstract A theory of two-dimensional arrays of coupled quantum dots in transverse magnetic fields is described. These systems are expected to exhibit exotic Hofstadter-like spectral and transport properties at modest magnetic fields ≥1 Tesla. They are shown to support intricate spectra of normal and “counter-rotating” magnetic edge states. The edge states are predicted to give rise to positive, negative and fractional quantum Hall plateaus in ballistic arrays coupled to ideal reservoirs. The fractions differ in value and origin from the usual fractional quantum Hall effect. In non-ballistic, macroscopic systems we predict integer positive and negative quantum Hall plateaus only, as in earlier theories of electrons in periodic 2D systems. This is understood in terms of “directed localization”, a generalization of Anderson localization to disordered waveguides supporting different numbers of modes propagating in opposite directions. The sample quality requirements for observing these effects are found to be very stringent.

Quantum Hall effect and inter-edge-state tunneling within a barrier.

We have introduced a controllable nano-scale incursion into a potential barrier imposed across a two-dimensional electron gas, and report on the phenomena that we observe as the incursion develops. In the quantum Hall regime, the conductance of this system displays quantized plateaus, broad minima and oscillations. We explain these features and their evolution with electrostatic potential geometry and magnetic field as a progression of current patterns formed by tunneling between edge and localized states within the barrier.

Artificial Impurities in Quantum Wires and Dots

One of the most common procedures employed in the fabrication of semiconductor nanostructures is the split-gate technique, first developed by (1986). Submicron metallic gates are deposited on top of the semiconductor crystal [usually about 90 nm above the two dimensional electron gas (2DEG)] and are used to electrostatically define the nanostructure. Electrical contact is easily made to these ‘top’ gates in a region away from the nanostructure where they can be widened enough to accommodate the connecting wire. This technique allows important experimental parameters (such as potential barrier heights) to be controlled by varying the applied gate voltage. It has led to the observation of several novel effects including the quantization of the conductance of quantum point contacts (Wharam et al., 1988; van Wees et al., 1988). Recently we have added a new element to the split gate technology, i.e. the ability to contact ‘isolated’ submicron gates (or alternatively isolated ohmic contacts) (Feng et al., 1993).

Can distributed currents be measured

Abstract We examine the possibility of measuring interior or “distributed” currents in quantum Hall systems by examining the transport problem for geometries which isolate the distributed current with a contact. We show that regardless of the geometry of the particular sample and contacts, the distributed current is not detected in the quantum Hall regime.