67 research outputs found
High Frequency Conductivity in the Quantum Hall Regime
We have measured the complex conductivity 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 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
. Even for large filing factor distances from the critical
point we find with a scaling exponent
Hopping conductivity in the quantum Hall effect -- revival of universal scaling
We have measured the temperature dependence of the conductivity
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 from this experiment. We
use our results to study the scaling behavior of as a function of the
filling factor distance to the critical point of the transition.
We find for all samples a power-law behavior
with a universal scaling exponent as proposed theoretically
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 , which governs the temperature dependence of
the fluctuations, is surprisingly different from the scaling length
governing the width of the quantum Hall plateau
transition
Direct Measurement of the g-Factor of Composite Fermions
The activation gap of the fractional quantum Hall states at constant
fillings and 2/5 has been measured as a function of the
perpendicular magnetic field . A linear dependence of on is
observed while approaching the spin polarization transition. This feature
allows a direct measurement of the -factor of composite fermions which
appears to be heavily renormalized by interactions and strongly sensitive to
the electronic filling factor.Comment: 4 pages, 4 figures Changed content: Fokus more on g-factors (and less
on other details
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
Enhanced Shot Noise in Tunneling through a Stack of Coupled Quantum Dots
We have investigated the noise properties of the tunneling current through
vertically coupled self-assembled InAs quantum dots. We observe
super-Poissonian shot noise at low temperatures. For increased temperature this
effect is suppressed. The super-Poissonian noise is explained by capacitive
coupling between different stacks of quantum dots
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