Hopping conductivity in the quantum Hall effect -- revival of universal scaling

We have measured the temperature dependence of the conductivity $\sigma_{xx}$ of a two-dimensional electron system deep into the localized regime of the quantum Hall plateau transition. Using variable-range hopping theory we are able to extract directly the localization length $\xi$ from this experiment. We use our results to study the scaling behavior of $\xi$ as a function of the filling factor distance $|\delta \nu|$ to the critical point of the transition. We find for all samples a power-law behavior $\xi\propto|\delta\nu|^{-\gamma}$ with a universal scaling exponent $\gamma = 2.3$ as proposed theoretically

High Frequency Conductivity in the Quantum Hall Regime

We have measured the complex conductivity $\sigma_{xx}$ of a two-dimensional electron system in the quantum Hall regime up to frequencies of 6 GHz at electron temperatures below 100 mK. Using both its imaginary and real part we show that $\sigma_{xx}$ can be scaled to a single function for different frequencies and for all investigated transitions between plateaus in the quantum Hall effect. Additionally, the conductivity in the variable-range hopping regime is used for a direct evaluation of the localization length $\xi$. Even for large filing factor distances $\delta \nu$ from the critical point we find $\xi \propto \delta \nu^{-\gamma}$ with a scaling exponent $\gamma=2.3$

Conductance fluctuations at the quantum Hall plateau transition

We analyze the conductance fluctuations observed in the quantum Hall regime for a bulk two-dimensional electron system in a Corbino geometry. We find that characteristics like the power spectral density and the temperature dependence agree well with simple expectations for universal conductance fluctuations in metals, while the observed amplitude is reduced. In addition, the dephasing length $L_\Phi \propto T^{-1/2}$, which governs the temperature dependence of the fluctuations, is surprisingly different from the scaling length $L_{sc}\propto T^{-1}$ governing the width of the quantum Hall plateau transition

Multiple transitions of the spin configuration in quantum dots

Single electron tunneling is studied in a many electron quantum dot in high magnetic fields. For such a system multiple transitions of the spin configuration are theoretically predicted. With a combination of spin blockade and Kondo effect we are able to detect five regions with different spin configurations. Transitions are induced with changing electron numbers.Comment: 4 pages, 5 figure

Spin noise spectroscopy in GaAs

We observe the noise spectrum of electron spins in bulk GaAs by Faraday rotation noise spectroscopy. The experimental technique enables the undisturbed measurement of the electron spin dynamics in semiconductors. We measure exemplarily the electron spin relaxation time and the electron Lande g-factor in n-doped GaAs at low temperatures and find good agreement of the measured noise spectrum with an unpretentious theory based on Poisson distribution probability.Comment: 4 pages, 4 figure

Non-invasive detection of molecular bonds in quantum dots

We performed charge detection on a lateral triple quantum dot with star-like geometry. The setup allows us to interpret the results in terms of two double dots with one common dot. One double dot features weak tunnel coupling and can be understood with atom-like electronic states, the other one is strongly coupled forming molecule-like states. In nonlinear measurements we identified patterns that can be analyzed in terms of the symmetry of tunneling rates. Those patterns strongly depend on the strength of interdot tunnel coupling and are completely different for atomic- or molecule-like coupled quantum dots allowing the non-invasive detection of molecular bonds.Comment: 4 pages, 4 figure