Measuring carrier density in parallel conduction layers of quantum Hall systems

An experimental analysis for two parallel conducting layers determines the full resistivity tensor of the parallel layer, at magnetic fields where the other layer is in the quantum Hall regime. In heterostructures which exhibit parallel conduction in the modulation-doped layer, this analysis quantitatively determines the charge density in the doping layer and can be used to estimate the mobility. To illustrate one application, experimental data show magnetic freeze-out of parallel conduction in a modulation doped heterojunction. As another example, the carrier density of a minimally populated second subband in a two-subband quantum well is determined. A simple formula is derived that can estimate the carrier density in a highly resistive parallel layer from a single Hall measurement of the total system.Comment: 7 pages, 7 figure

Rayleigh-Benard Convection with a Radial Ramp in Plate Separation

Pattern formation in Rayleigh-Benard convection in a large-aspect-ratio cylinder with a radial ramp in the plate separation is studied analytically and numerically by performing numerical simulations of the Boussinesq equations. A horizontal mean flow and a vertical large scale counterflow are quantified and used to understand the pattern wavenumber. Our results suggest that the mean flow, generated by amplitude gradients, plays an important role in the roll compression observed as the control parameter is increased. Near threshold the mean flow has a quadrupole dependence with a single vortex in each quadrant while away from threshold the mean flow exhibits an octupole dependence with a counter-rotating pair of vortices in each quadrant. This is confirmed analytically using the amplitude equation and Cross-Newell mean flow equation. By performing numerical experiments the large scale counterflow is also found to aid in the roll compression away from threshold but to a much lesser degree. Our results yield an understanding of the pattern wavenumbers observed in experiment away from threshold and suggest that near threshold the mean flow and large scale counterflow are not responsible for the observed shift to smaller than critical wavenumbers.Comment: 10 pages, 13 figure

Extensive chaos in Rayleigh-Bénard convection

Using large-scale numerical calculations we explore spatiotemporal chaos in Rayleigh-Bénard convection for experimentally relevant conditions. We calculate the spectrum of Lyapunov exponents and the Lyapunov dimension describing the chaotic dynamics of the convective fluid layer at constant thermal driving over a range of finite system sizes. Our results reveal that the dynamics of fluid convection is truly chaotic for experimental conditions as illustrated by a positive leading-order Lyapunov exponent. We also find the chaos to be extensive over the range of finite-sized systems investigated as indicated by a linear scaling between the Lyapunov dimension of the chaotic attractor and the system size

Four-point measurements of n- and p-type two-dimensional systems fabricated with cleaved-edge overgrowth

We demonstrate a contact design that allows four-terminal magnetotransport measurements of cleaved-edge overgrown two-dimensional electron and hole systems. By lithographically patterning and etching a bulk-doped surface layer, finger-shaped leads are fabricated, which contact the two-dimensional systems on the cleave facet. Both n- and p-type two-dimensional systems are demonstrated at the cleaved edge, using Si as either donor or acceptor, dependent on the growth conditions. Four-point measurements of both gated and modulation-doped samples yield fractional quantum Hall features for both n- and p-type, with several higher-order fractions evident in n-type modulation-doped samples.Comment: 3 pages, 3 figure

The perplexing continuum slope of Mars: Effects of thin ferric coatings and viewing geometry

The experiment discussed here was designed to constrain interpretations of variations in continuum slope variations which define several spectral annuli on the flanks of Olympus Mons, observed in the Imaging Spectrometer (IMS) data. The IMS Olympus Mons data reveal that the rings, seen as alternating brighter and darker reflectance in Viking data, correspond to annuli of alternating shallower and steeper continuum slope. At least three factors contributing to continuum slope are identified: ferric coating thickness, viewing geometry, and surface texture. Because the Olympus Mons spectral annuli were observed at nearly constant backscatter geometries in the ISM data, with only slight viewing variations due to the volcanoe's flank slopes, the difference of continuum slope between annuli probably cannot be explained by viewing geometry alone. This suggests that the variation of some fundamental surface characteristics, such as ferric dust/rind thickness or surface texture, is the cause of the Olympus Mons special annuli observed in the ISM imaging spectrometer data

Traveling waves in rotating Rayleigh-Bénard convection: Analysis of modes and mean flow

Numerical simulations of the Boussinesq equations with rotation for realistic no-slip boundary conditions and a finite annular domain are presented. These simulations reproduce traveling waves observed experimentally. Traveling waves are studied near threshhold by using the complex Ginzburg-Landau equation (CGLE): a mode analysis enables the CGLE coefficients to be determined. The CGLE coefficients are compared with previous experimental and theoretical results. Mean flows are also computed and found to be more significant as the Prandtl number decreases (from sigma=6.4 to sigma=1). In addition, the mean flow around the outer radius of the annulus appears to be correlated with the mean flow around the inner radius