Non-Universal Behavior of Finite Quantum Hall Systems as a Result of Weak Macroscopic Inhomogeneities

We show that, at low temperatures, macroscopic inhomogeneities of the electron density in the interior of a finite sample cause a reduction in the measured conductivity peak heights $\sigma_{xx}^{\rm max}$ compared to the universal values previously predicted for infinite homogeneous samples. This effect is expected to occur for the conductivity peaks measured in standard experimental geometries such as the Hall bar and the Corbino disc. At the lowest temperatures, the decrease in $\sigma_{xx}^{\rm max}(T)$ is found to saturate at values proportional to the difference between the adjacent plateaus in $\sigma_{xy}$, with a prefactor which depends on the particular realization of disorder in the sample. We argue that this provides a possible explanation of the ``non-universal scaling'' of $\sigma_{xx}^{\rm max}$ observed in a number of experiments. We also predict an enhancement of the ``non-local'' resistance due to the macroscopic inhomogeneities. We argue that, in the Hall bar with a sharp edge, the enhanced ``non-local'' resistance and the size corrections to the ``local'' resistance $R_{xx}$ are directly related. Using this relation, we suggest a method by which the finite-size corrections may be eliminated from $R_{xx}$ and $R_{xy}$ in this case.Comment: REVTEX 3.0 file (38 pages) + 5 postscript figures in uuencoded format. Revised version includes an additional figure showing unpublished experimental dat

Resistivity peak values at transition between fractional quantum Hall states

Experimental data available in the literature for peak values of the diagonal resistivity in the transitions between fractional quantum Hall states are compared with the theoretical predictions. It is found that the majority of the peak values are close to the theoretical values for two-dimensional systems with moderate mobilities.Comment: 3 pages, 1 figur

Comparison of radiation damage in silicon induced by proton and neutron irradiation

The subject of radiation damage to Si detectors induced by 24-GeV/c protons and nuclear reactor neutrons has been studied. Detectors fabricated on single-crystal silicon enriched with various impurities have been tested. Significant differences in electrically active defects have been found between the various types of material. The results of the study suggest for the first time that the widely used nonionizing energy loss (NIEL) factors are insufficient for normalization of the electrically active damage in case of oxygen- and carbon-enriched silicon detectors. It has been found that a deliberate introduction of impurities into the semiconductor can affect the radiation hardness of silicon detectors. (16 refs)

A different view of the quantum Hall plateau-to-plateau transitions

We demonstrate experimentally that the transitions between adjacent integer quantum Hall (QH) states are equivalent to a QH-to-insulator transition occurring in the top Landau level, in the presence of an inert background of the other completely filled Landau levels, each contributing a single unit of quantum conductance, $e^{2}/h$, to the total Hall conductance of the system.Comment: 10 pages, 4 figures, Revtex 3.

Derivative relation for thermopower in the quantum Hall regime

Recently, Tieke et al (to be published in PRL) have observed the relation S_{yx} = alpha B dS_{xx}/dB for the components of the thermopower tensor in the quantum Hall regime, where alpha is a constant and B is the magnetic field. Simon and Halperin (PRL 73, 3278 (1994)) have suggested that an analogous relation observed for the resistivity tensor R_{xx} = \alpha B dR_{xy}/dB can be explained with a model of classical transport in an inhomogeneous medium where the local Hall resistivity is a function of position and the local dissipative resistivity is a small constant. In the present paper, we show that this new thermopower relation can be explained with a similar model.Comment: This paper supercedes cond-mat/9705001 which was withdrawn. 4 pages, Revte

Universality in an integer Quantum Hall transition

An integer Quantum Hall effect transition is studied in a modulation doped p-SiGe sample. In contrast to most examples of such transitions the longitudinal and Hall conductivities at the critical point are close to 0.5 and 1.5 (e^2/h), the theoretically expected values. This allows the extraction of a scattering parameter, describing both conductivity components, which depends exponentially on filling factor. The strong similarity of this functional form to those observed for transitions into the Hall insulating state and for the B=0 metal- insulator transition implies a universal quantum critical behaviour for the transitions. The observation of this behaviour in the integer Quantum Hall effect, for this particular sample, is attributed to the short-ranged character of the potential associated with the dominant scatterers

Effective action and interaction energy of coupled quantum dots

We obtain the effective action of tunnel-coupled quantum dots, by modeling the system as a Luttinger liquid with multiple barriers. For a double dot system, we find that the resonance conditions for perfect conductance form a hexagon in the plane of the two gate voltages controlling the density of electrons in each dot. We also explicitly obtain the functional dependence of the interaction energy and peak-splitting on the gate voltage controlling tunneling between the dots and their charging energies. Our results are in good agreement with recent experimental results, from which we obtain the Luttinger interaction parameter $K=0.74$.Comment: 5 pgs,latex,3 figs,revised version to be publshed in Phys.Rev.

Universality in the Crossover between Edge Channel and Bulk Transport in the Quantum Hall Regime

We present a new theoretical approach for the integer quantum Hall effect, which is able to describe the inter-plateau transitions as well as the transition to the Hall insulator. We find two regimes (metallic and insulator like) of the top Landau level, in which the dissipative bulk current appears in different directions. The regimes are separated by a temperature invariant point.Comment: 4 page, 2 eps figures included, submitte

Thermodynamic and Tunneling Density of States of the Integer Quantum Hall Critical State

We examine the long wave length limit of the self-consistent Hartree-Fock approximation irreducible static density-density response function by evaluating the charge induced by an external charge. Our results are consistent with the compressibility sum rule and inconsistent with earlier work that did not account for consistency between the exchange-local-field and the disorder potential. We conclude that the thermodynamic density of states is finite, in spite of the vanishing tunneling density of states at the critical energy of the integer quantum Hall transition.Comment: 5 pages, 4 figures, minor revisions, published versio