178 research outputs found
The microscopic nature of localization in the quantum Hall effect
The quantum Hall effect arises from the interplay between localized and
extended states that form when electrons, confined to two dimensions, are
subject to a perpendicular magnetic field. The effect involves exact
quantization of all the electronic transport properties due to particle
localization. In the conventional theory of the quantum Hall effect,
strong-field localization is associated with a single-particle drift motion of
electrons along contours of constant disorder potential. Transport experiments
that probe the extended states in the transition regions between quantum Hall
phases have been used to test both the theory and its implications for quantum
Hall phase transitions. Although several experiments on highly disordered
samples have affirmed the validity of the single-particle picture, other
experiments and some recent theories have found deviations from the predicted
universal behaviour. Here we use a scanning single-electron transistor to probe
the individual localized states, which we find to be strikingly different from
the predictions of single-particle theory. The states are mainly determined by
Coulomb interactions, and appear only when quantization of kinetic energy
limits the screening ability of electrons. We conclude that the quantum Hall
effect has a greater diversity of regimes and phase transitions than predicted
by the single-particle framework. Our experiments suggest a unified picture of
localization in which the single-particle model is valid only in the limit of
strong disorder
On fractionality of the path packing problem
In this paper, we study fractional multiflows in undirected graphs. A
fractional multiflow in a graph G with a node subset T, called terminals, is a
collection of weighted paths with ends in T such that the total weights of
paths traversing each edge does not exceed 1. Well-known fractional path
packing problem consists of maximizing the total weight of paths with ends in a
subset S of TxT over all fractional multiflows. Together, G,T and S form a
network. A network is an Eulerian network if all nodes in N\T have even
degrees.
A term "fractionality" was defined for the fractional path packing problem by
A. Karzanov as the smallest natural number D so that there exists a solution to
the problem that becomes integer-valued when multiplied by D. A. Karzanov has
defined the class of Eulerian networks in terms of T and S, outside which D is
infinite and proved that whithin this class D can be 1,2 or 4. He conjectured
that D should be 1 or 2 for this class of networks. In this paper we prove this
conjecture.Comment: 18 pages, 5 figures in .eps format, 2 latex files, main file is
kc13.tex Resubmission due to incorrectly specified CS type of the article; no
changes to the context have been mad
Compressibility of a two-dimensional hole gas in tilted magnetic field
We have measured compressibility of a two-dimensional hole gas in
p-GaAs/AlGaAs heterostructure, grown on a (100) surface, in the presence of a
tilted magnetic field. It turns out that the parallel component of magnetic
field affects neither the spin splitting nor the density of states. We conclude
that: (a) g-factor in the parallel magnetic field is nearly zero in this
system; and (b) the level of the disorder potential is not sensitive to the
parallel component of the magnetic field
Physics of the Insulating Phase in the Dilute Two-Dimensional Electron Gas
We propose to use the radio-frequency single-electron transistor as an
extremely sensitive probe to detect the time-periodic ac signal generated by
sliding electron lattice in the insulating state of the dilute two-dimensional
electron gas. We also propose to use the optically-pumped NMR technique to
probe the electron spin structure of the insulating state. We show that the
electron effective mass and spin susceptibility are strongly enhanced by
critical fluctuations of electron lattice in the vicinity of the
metal-insulator transition, as observed in experiment.Comment: 5 pages, 2 figures, uses jetpl.cls (included). v.4: After publication
in JETP Letters, two plots comparing theory and experiment are added, and a
minor error is correcte
A self-consistent theory for graphene transport
We demonstrate theoretically that most of the observed transport properties
of graphene sheets at zero magnetic field can be explained by scattering from
charged impurities. We find that, contrary to common perception, these
properties are not universal but depend on the concentration of charged
impurities . For dirty samples (), the value of the minimum
conductivity at low carrier density is indeed in agreement with early
experiments, with weak dependence on impurity concentration. For cleaner
samples, we predict that the minimum conductivity depends strongly on , increasing to for . A clear strategy to improve graphene mobility is to eliminate
charged impurities or use a substrate with a larger dielectric constant.Comment: To be published in Proc. Natl. Acad. Sci. US
Quantum Capacitance Extraction for Carbon Nanotube Interconnects
Electrical transport in metallic carbon nanotubes, especially the ones with diameters of the order of a few nanometers can be best described using the Tomanaga Luttinger liquid (TL) model. Recently, the TL model has been used to create a convenient transmission line like phenomenological model for carbon nanotubes. In this paper, we have characterized metallic nanotubes based on that model, quantifying the quantum capacitances of individual metallic single walled carbon nanotubes and crystalline bundles of single walled tubes of different diameters. Our calculations show that the quantum capacitances for both individual tubes and the bundles show a weak dependence on the diameters of their constituent tubes. The nanotube bundles exhibit a significantly large quantum capacitance due to enhancement of density of states at the Fermi level
Recommended from our members
A group contribution model for determining the sublimation enthalpy of organic compounds at the standard reference temperature of 298 K
Article discussing a group contribution model for determining the sublimation enthalpy of organic compounds at the standard reference temperature of 298 K
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A Group Contribution Model for Determining the Vaporization Enthalpy of Organic Compounds at the Standard Reference Temperature of 298 K
Article on a group contribution model for determining the vaporization enthalpy of organic compounds at the standard reference temperature of 298 K
The nature of localization in graphene under quantum Hall conditions
Particle localization is an essential ingredient in quantum Hall physics
[1,2]. In conventional high mobility two-dimensional electron systems Coulomb
interactions were shown to compete with disorder and to play a central role in
particle localization [3]. Here we address the nature of localization in
graphene where the carrier mobility, quantifying the disorder, is two to four
orders of magnitude smaller [4,5,6,7,8,9,10]. We image the electronic density
of states and the localized state spectrum of a graphene flake in the quantum
Hall regime with a scanning single electron transistor [11]. Our microscopic
approach provides direct insight into the nature of localization. Surprisingly,
despite strong disorder, our findings indicate that localization in graphene is
not dominated by single particle physics, but rather by a competition between
the underlying disorder potential and the repulsive Coulomb interaction
responsible for screening.Comment: 18 pages, including 5 figure
On the Ground State of Electron Gases at Negative Compressibility
Two- and three-dimensional electron gases with a uniform neutralizing
background are studied at negative compressibility. Parametrized expressions
for the dielectric function are used to access this strong-coupling regime,
where the screened Coulomb potential becomes overall attractive for like
charges. Closely examining these expressions reveals that the ground state with
a periodic modulation of the charge density, albeit exponentially damped,
replaces the homogeneous one at positive compressibility. The wavevector
characterizing the new ground state depends on the density and is complex,
having a positive imaginary part, as does the homogeneous ground state, and
real part, as does the genuine charge density wave.Comment: 6 double-column pages, 2 figures. 2nd version is an extension of the
1st one, giving more detail
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