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

The Quantized Hall Insulator: A New Insulator in Two-Dimensions

Quite generally, an insulator is theoretically defined by a vanishing conductivity tensor at the absolute zero of temperature. In classical insulators, such as band insulators, vanishing conductivities lead to diverging resistivities. In other insulators, in particular when a high magnetic field (B) is added, it is possible that while the magneto-resistance diverges, the Hall resistance remains finite, which is known as a Hall insulator. In this letter we demonstrate experimentally the existence of another, more exotic, insulator. This insulator, which terminates the quantum Hall effect series in a two-dimensional electron system, is characterized by a Hall resistance which is approximately quantized in the quantum unit of resistance h/e^2. This insulator is termed a quantized Hall insulator. In addition we show that for the same sample, the insulating state preceding the QHE series, at low-B, is of the HI kind.Comment: 4 page

Excessive noise as a test for many-body localization

Recent experimental reports suggested the existence of a finite-temperature insulator in the vicinity of the superconductor-insulator transition. The rapid decay of conductivity over a narrow temperature range was theoretically linked to both a finite-temperature transition to a many-body-localized state, and to a charge-Berezinskii-Kosterlitz-Thouless transition. Here we report of low-frequency noise measurements of such insulators to test for many-body localization. We observed a huge enhancement of the low-temperatures noise when exceeding a threshold voltage for nonlinear conductivity and discuss our results in light of the theoretical models

Universality at integer quantum Hall transitions

We report in this paper results of experimental and theoretical studies of transitions between different integer quantum Hall phases, as well as transition between the insulating phase and quantum Hall phases at high magnetic fields. We focus mainly on universal properties of the transitions. We demonstrate that properly defined conductivity tensor is universal at the transitions. We also present numerical results of a non-interacting electron model, which suggest that the Thouless conductance is universal at integer quantum Hall transitions, just like the conductivity tensor. Finite temperature and system size effects near the transition point are also studied.Comment: 20 pages, 15 figure

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

Time-Dependent Random Walks and the Theory of Complex Adaptive Systems

Motivated by novel results in the theory of complex adaptive systems, we analyze the dynamics of random walks in which the jumping probabilities are {\it time-dependent}. We determine the survival probability in the presence of an absorbing boundary. For an unbiased walk the survival probability is maximized in the case of large temporal oscillations in the jumping probabilities. On the other hand, a random walker who is drifted towards the absorbing boundary performs best with a constant jumping probability. We use the results to reveal the underlying dynamics responsible for the phenomenon of self-segregation and clustering observed in the evolutionary minority game.Comment: 5 pages, 2 figure

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

Symmetry in the insulator - quantum Hall - insulator transitions observed in a Ge/SiGe quantum well

We examine the magnetic field driven insulator-quantum Hall-insulator transitions of the two dimensional hole gas in a Ge/SiGe quantum well. We observe direct transitions between low and high magnetic field insulators and the $\nu=1$ quantum Hall state. With increasing magnetic field, the transitions from insulating to quantum Hall and quantum Hall to insulating are very similar with respect to their transport properties. We address the temperature dependence around the transitions and show that the characteristic energy scale for the high field transition is larger.Comment: 4 page

Phase Diagram of Integer Quantum Hall Effect

The phase diagram of integer quantum Hall effect is numerically determined in the tight-binding model, which can account for overall features of recently obtained experimental phase diagram. In particular, the quantum Hall plateaus are terminated by two distinct insulating phases, characterized by the Hall resistance with classic and quantized values, respectively, which is also in good agreement with experiments.Comment: 4 pages, RevTex, 4 PostScript figures; one new figure is added; minor modifications in the tex