Noise at a Fermi-edge singularity

We present noise measurements of self-assembled InAs quantum dots at high magnetic fields. In comparison to I-V characteristics at zero magnetic field we notice a strong current overshoot which is due to a Fermi-edge singularity. We observe an enhanced suppression in the shot noise power simultaneous to the current overshoot which is attributed to the electron-electron interaction in the Fermi-edge singularity

Noise enhancement due to quantum coherence in coupled quantum dots

We show that the intriguing observation of noise enhancement in the charge transport through two vertically coupled quantum dots can be explained by the interplay of quantum coherence and strong Coulomb blockade. We demonstrate that this novel mechanism for super-Poissonian charge transfer is very sensitive to decoherence caused by electron-phonon scattering as inferred from the measured temperature dependence.Comment: 4 pages, 3 figures, corrected version (Figs.2 and 3

Universal oscillations in counting statistics

Noise is a result of stochastic processes that originate from quantum or classical sources. Higher-order cumulants of the probability distribution underlying the stochastic events are believed to contain details that characterize the correlations within a given noise source and its interaction with the environment, but they are often difficult to measure. Here we report measurements of the transient cumulants > of the number n of passed charges to very high orders (up to m=15) for electron transport through a quantum dot. For large m, the cumulants display striking oscillations as functions of measurement time with magnitudes that grow factorially with m. Using mathematical properties of high-order derivatives in the complex plane we show that the oscillations of the cumulants in fact constitute a universal phenomenon, appearing as functions of almost any parameter, including time in the transient regime. These ubiquitous oscillations and the factorial growth are system-independent and our theory provides a unified interpretation of previous theoretical studies of high-order cumulants as well as our new experimental data.Comment: 19 pages, 4 figures, final version as published in PNA

Dynamical scaling of the quantum Hall plateau transition

Using different experimental techniques we examine the dynamical scaling of the quantum Hall plateau transition in a frequency range f = 0.1-55 GHz. We present a scheme that allows for a simultaneous scaling analysis of these experiments and all other data in literature. We observe a universal scaling function with an exponent kappa = 0.5 +/- 0.1, yielding a dynamical exponent z = 0.9 +/- 0.2.Comment: v2: Length shortened to fulfil Journal criteri

A Farewell to Liouvillians

We examine the Liouvillian approach to the quantum Hall plateau transition, as introduced recently by Sinova, Meden, and Girvin [Phys. Rev. B {\bf 62}, 2008 (2000)] and developed by Moore, Sinova and Zee [Phys. Rev. Lett. {\bf 87}, 046801 (2001)]. We show that, despite appearances to the contrary, the Liouvillian approach is not specific to the quantum mechanics of particles moving in a single Landau level: we formulate it for a general disordered single-particle Hamiltonian. We next examine the relationship between Liouvillian perturbation theory and conventional calculations of disorder-averaged products of Green functions and show that each term in Liouvillian perturbation theory corresponds to a specific contribution to the two-particle Green function. As a consequence, any Liouvillian approximation scheme may be re-expressed in the language of Green functions. We illustrate these ideas by applying Liouvillian methods, including their extension to $N_L > 1$ Liouvillian flavors, to random matrix ensembles, using numerical calculations for small integer $N_L$ and an analytic analysis for large $N_L$. We find that behavior at $N_L > 1$ is different in qualitative ways from that at $N_L=1$. In particular, the $N_L = \infty$ limit expressed using Green functions generates a pathological approximation, in which two-particle correlation functions fail to factorize correctly at large separations of their energy, and exhibit spurious singularities inside the band of random matrix energy levels. We also consider the large $N_L$ treatment of the quantum Hall plateau transition, showing that the same undesirable features are present there, too

A New Spin-Orbit Induced Universality Class in the Quantum Hall Regime ?

Using heuristic arguments and numerical simulations it is argued that the critical exponent $\nu$ describing the localization length divergence at the quantum Hall transition is modified in the presence of spin-orbit scattering with short range correlations. The exponent is very close to $\nu=4/3$, the percolation correlation length exponent, the prediction of a semi-classical argument. In addition, a region of weakly localized regime, where the localization length is exponentially large, is conjectured.Comment: 4 two-column pages including 4 eps figure

Generation of energy selective excitations in quantum Hall edge states

We operate an on-demand source of single electrons in high perpendicular magnetic fields up to 30T, corresponding to a filling factor below 1/3. The device extracts and emits single charges at a tunable energy from and to a two-dimensional electron gas, brought into well defined integer and fractional quantum Hall (QH) states. It can therefore be used for sensitive electrical transport studies, e.g. of excitations and relaxation processes in QH edge states

Shot noise in resonant tunneling through a zero-dimensional state with a complex energy spectrum

We investigate the noise properties of a GaAs/AlGaAs resonant tunneling structure at bias voltages where the current characteristic is determined by single electron tunneling. We discuss the suppression of the shot noise in the framework of a coupled two-state system. For large bias voltages we observed super-Poissonian shot noise up to values of the Fano factor $\alpha \approx 10$.Comment: 4 pages, 4 figures, accepted for Phys. Rev.

Dimensional Crossover of Localisation and Delocalisation in a Quantum Hall Bar

The 2-- to 1--dimensional crossover of the localisation length of electrons confined to a disordered quantum wire of finite width $L_y$ is studied in a model of electrons moving in the potential of uncorrelated impurities. An analytical formula for the localisation length is derived, describing the dimensional crossover as function of width $L_y$, conductance $g$ and perpendicular magnetic field $B$ . On the basis of these results, the scaling analysis of the quantum Hall effect in high Landau levels, and the delocalisation transition in a quantum Hall wire are reconsidered.Comment: 12 pages, 7 figure