The quantized Hall effect in the presence of resistance fluctuations

We present an experimental study of mesoscopic, two-dimensional electronic systems at high magnetic fields. Our samples, prepared from a low-mobility InGaAs/InAlAs wafer, exhibit reproducible, sample specific, resistance fluctuations. Focusing on the lowest Landau level we find that, while the diagonal resistivity displays strong fluctuations, the Hall resistivity is free of fluctuations and remains quantized at its $\nu=1$ value, $h/e^{2}$. This is true also in the insulating phase that terminates the quantum Hall series. These results extend the validity of the semicircle law of conductivity in the quantum Hall effect to the mesoscopic regime.Comment: Includes more data, changed discussio

Mesoscopic oscillations of the conductance of disordered metallic samples as a function of temperature

We show theoretically and experimentally that the conductance of small disordered samples exhibits random oscillations as a function of temperature. The amplitude of the oscillations decays as a power law of temperature, and their characteristic period is of the order of the temperature itself

Visibility diagrams and experimental stripe structure in the quantum Hall effect

We analyze various properties of the visibility diagrams that can be used in the context of modular symmetries and confront them to some recent experimental developments in the Quantum Hall Effect. We show that a suitable physical interpretation of the visibility diagrams which permits one to describe successfully the observed architecture of the Quantum Hall states gives rise naturally to a stripe structure reproducing some of the experimental features that have been observed in the study of the quantum fluctuations of the Hall conductance. Furthermore, we exhibit new properties of the visibility diagrams stemming from the structure of subgroups of the full modular group.Comment: 8 pages in plain TeX, 7 figures in a single postscript fil

Two-terminal conductance fluctuations in the integer quantum Hall regime

Motivated by recent experiments on the conductance fluctuations in mesoscopic integr quantum Hall systems, we consider a model in which the Coulomb interactions are incorporated into the picture of edge-state transport through a single saddle-point. The occupancies of `classical' localised states in the two-dimensional electron system change due to the interactions between electrons when the gate voltage on top of the device is varied. The electrostatic potential between the localised states and the saddle-point causes fluctuations of the saddle-point potential and thus fluctuations of the transmission probability of edge states. This simple model is studied numerically and compared with the observation.Comment: 6 pages with 3 figures. To be published in Physical Review

Finite-temperature Fermi-edge singularity in tunneling studied using random telegraph signals

We show that random telegraph signals in metal-oxide-silicon transistors at millikelvin temperatures provide a powerful means of investigating tunneling between a two-dimensional electron gas and a single defect state. The tunneling rate shows a peak when the defect level lines up with the Fermi energy, in excellent agreement with theory of the Fermi-edge singularity at finite temperature. This theory also indicates that defect levels are the origin of the dissipative two-state systems observed previously in similar devices.Comment: 5 pages, REVTEX, 3 postscript figures included with epsfi

Phase transitions on the surface of a carbon nanotube

A suspended carbon nanotube can act as a nanoscale resonator with remarkable electromechanical properties and the ability to detect adsorption on its surface at the level of single atoms. Understanding adsorption on nanotubes and other graphitic materials is key to many sensing and storage applications. Here we show that nanotube resonators offer a powerful new means of investigating fundamental aspects of adsorption on carbon, including the collective behaviour of adsorbed matter and its coupling to the substrate electrons. By monitoring the vibrational resonance frequency in the presence of noble gases, we observe the formation of monolayers on the cylindrical surface and phase transitions within these monolayers, and simultaneous modification of the electrical conductance. The monolayer observations also demonstrate the possibility of studying the fundamental behaviour of matter in cylindrical geometry.Comment: Unpublished; 7 pages with 4 figures plus 3 pages of supplementary materia

Current carrying capacity of carbon nanotubes

The current carrying capacity of ballistic electrons in carbon nanotubes that are coupled to ideal contacts is analyzed. At small applied voltages, where electrons are injected only into crossing subbands, the differential conductance is $4e^2/h$. At applied voltages larger than $\Delta E_{NC}/2e$ ($\Delta E_{NC}$ is the energy level spacing of first non crossing subbands), electrons are injected into non crossing subbands. The contribution of these electrons to current is determined by the competing processes of Bragg reflection and Zener type inter subband tunneling. In small diameter nanotubes, Bragg reflection dominates, and the maximum differential conductance is comparable to $4e^2/h$. Inter subband Zener tunneling can be non negligible as the nanotube diameter increases because $\Delta E_{NC}$ is inversely proportional to the diameter. As a result, with increasing nanotube diameter, the differential conductance becomes larger than $4e^2/h$, though not comparable to the large number of subbands into which electrons are injected from the contacts. These results may be relevant to recent experiments in large diameter multi-wall nanotubes that observed conductances larger than $4e^2/h$.Comment: 12 pages, 4 figure