39 research outputs found
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 Liouvillian flavors, to random matrix ensembles, using numerical
calculations for small integer and an analytic analysis for large .
We find that behavior at is different in qualitative ways from that
at . In particular, the 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 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 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 , 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
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 .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 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 , conductance and
perpendicular magnetic field . 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
Integer quantum Hall transition in the presence of a long-range-correlated quenched disorder
We theoretically study the effect of long-ranged inhomogeneities on the
critical properties of the integer quantum Hall transition. For this purpose we
employ the real-space renormalization-group (RG) approach to the network model
of the transition. We start by testing the accuracy of the RG approach in the
absence of inhomogeneities, and infer the correlation length exponent nu=2.39
from a broad conductance distribution. We then incorporate macroscopic
inhomogeneities into the RG procedure. Inhomogeneities are modeled by a smooth
random potential with a correlator which falls off with distance as a power
law, r^{-alpha}. Similar to the classical percolation, we observe an
enhancement of nu with decreasing alpha. Although the attainable system sizes
are large, they do not allow one to unambiguously identify a cusp in the
nu(alpha) dependence at alpha_c=2/nu, as might be expected from the extended
Harris criterion. We argue that the fundamental obstacle for the numerical
detection of a cusp in the quantum percolation is the implicit randomness in
the Aharonov-Bohm phases of the wave functions. This randomness emulates the
presence of a short-range disorder alongside the smooth potential.Comment: 10 pages including 6 figures, revised version as accepted for
publication in PR
Theta renormalization, electron-electron interactions and super universality in the quantum Hall regime
The renormalization theory of the quantum Hall effect relies primarily on the
non-perturbative concept of theta renormalization by instantons. Within the
generalized non-linear sigma model approach initiated by Finkelstein we obtain
the physical observables of the interacting electron gas, formulate the general
(topological) principles by which the Hall conductance is robustly quantized
and derive - for the first time - explicit expressions for the non-perturbative
(instanton) contributions to the renormalization group beta- and gamma-
functions. Our results are in complete agreement with the recently proposed
idea of super universality which says that the fundamental aspects of the
quantum Hall effect are all generic features the instanton vacuum concept in
asymptotically free field theory.Comment: ReVTeX, 38 pages, 9 figure