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

The origin of switching noise in GaAs/AlGaAs lateral gated devices

We have studied the origin of switching (telegraph) noise at low temperature in lateral quantum structures defined electrostatically in GaAs/AlGaAs heterostructures by surface gates. The noise was measured by monitoring the conductance fluctuations around $e^2/h$ on the first step of a quantum point contact at around 1.2 K. Cooling with a positive bias on the gates dramatically reduces this noise, while an asymmetric bias exacerbates it. We propose a model in which the noise originates from a leakage current of electrons that tunnel through the Schottky barrier under the gate into the doped layer. The key to reducing noise is to keep this barrier opaque under experimental conditions. Bias cooling reduces the density of ionized donors, which builds in an effective negative gate voltage. A smaller negative bias is therefore needed to reach the desired operating point. This suppresses tunnelling from the gate and hence the noise. The reduction in the density of ionized donors also strengthens the barrier to tunneling at a given applied voltage. Support for the model comes from our direct observation of the leakage current into a closed quantum dot, around $10^{-20} \mathrm{A}$ for this device. The current was detected by a neighboring quantum point contact, which showed monotonic steps in time associated with the tunneling of single electrons into the dot. If asymmetric gate voltages are applied, our model suggests that the noise will increase as a consequence of the more negative gate voltage applied to one of the gates to maintain the same device conductance. We observe exactly this behaviour in our experiments.Comment: 8 pages, 7 figure

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

Conductance Correlations Near Integer Quantum Hall Transitions

In a disordered mesoscopic system, the typical spacing between the peaks and the valleys of the conductance as a function of Fermi energy $E_F$ is called the conductance energy correlation range $E_c$. Under the ergodic hypothesis, the latter is determined by the half-width of the ensemble averaged conductance correlation function: $F=$. In ordinary diffusive metals, $E_c\sim D/L^2$, where $D$ is the diffusion constant and $L$ is the linear dimension of the phase-coherent sample. However, near a quantum phase transition driven by the location of the Fermi energy $E_F$, the above picture breaks down. As an example of the latter, we study, for the first time, the conductance correlations near the integer quantum Hall transitions of which $E_F$ is a critical coupling constant. We point out that the behavior of $F$ is determined by the interplay between the static and the dynamic properties of the critical phenomena.Comment: 4 pages, 4 figures, minor corrections, to appear in Phys. Rev. Let

Spin states of the first four holes in a silicon nanowire quantum dot

We report measurements on a silicon nanowire quantum dot with a clarity that allows for a complete understanding of the spin states of the first four holes. First, we show control of the hole number down to one. Detailed measurements at perpendicular magnetic fields reveal the Zeeman splitting of a single hole in silicon. We are able to determine the ground-state spin configuration for one to four holes occupying the quantum dot and find a spin filling with alternating spin-down and spin-up holes, which is confirmed by magnetospectroscopy up to 9T. Additionally, a so far inexplicable feature in single-charge quantum dots in many materials systems is analyzed in detail. We observe excitations of the zero-hole ground-state energy of the quantum dot, which cannot correspond to electronic or Zeeman states. We show that the most likely explanation is acoustic phonon emission to a cavity between the two contacts to the nanowire.Comment: 24 pages, 8 figures, both including supporting informatio