76 research outputs found
Vortex Deconfinement in the XY Model with a Magnetic Field
We study vortex unbinding for the classical two-dimensional XY model in a
magnetic field on square and triangular lattices. A renormalization group
analysis combined with duality in the model shows that at high temperature and
high field, the vortices unbind as the magnetic field is lowered in a two-step
process: strings of overturned spins first proliferate and then vortices
unbind. The transitions are highly continuous but are not of the
Kosterlitz-Thouless type. The unbound vortex fixed point is shown to inherit
properties of the underlying lattice, in particular containing a set of nodal
lines that reflect the lattice symmetry.Comment: RevTex, 2 column format. 13 figure
Power-law Kohn anomaly in undoped graphene induced by Coulomb interactions
Phonon dispersions generically display nonanalytic points, known as Kohn anomalies, due to electron-phonon interactions. We analyze this phenomenon for a zone-boundary phonon in undoped graphene. When electron-electron interactions with coupling constant \beta are taken into account, one observes behavior demonstrating that the electrons are in a critical phase: the phonon dispersion and lifetime develop power-law behavior with \beta-dependent exponents. The observation of this signature would allow experimental access to the critical properties of the electron state, and would provide a measure of its proximity to an excitonic insulating phase
Probing Vortex Unbinding via Dipole Fluctuations
We develop a numerical method for detecting a vortex unbinding transition in
a two-dimensional system by measuring large scale fluctuations in the total
vortex dipole moment of the system. These are characterized by a
quantity which measures the number of configurations in a simulation
for which the either or is half the system size. It is shown that
tends to a non-vanishing constant for large system sizes in the
unbound phase, and vanishes in the bound phase. The method is applied to the XY
model both in the absence and presence of a magnetic field. In the latter case,
the system size dependence of suggests that there exist three distinct
phases, one unbound vortex phase, a logarithmically bound phase, and a linearly
bound phase.Comment: 6 pages, 2 figure
Stripes in Quantum Hall Double Layer Systems
We present results of a study of double layer quantum Hall systems in which
each layer has a high-index Landau level that is half-filled. Hartree-Fock
calculations indicate that, above a critical layer separation, the system
becomes unstable to the formation of a unidirectional coherent charge density
wave (UCCDW), which is related to stripe states in single layer systems. The
UCCDW state supports a quantized Hall effect when there is tunneling between
layers, and is {\it always} stable against formation of an isotropic Wigner
crystal for Landau indices . The state does become unstable to the
formation of modulations within the stripes at large enough layer separation.
The UCCDW state supports low-energy modes associated with interlayer coherence.
The coherence allows the formation of charged soliton excitations, which become
gapless in the limit of vanishing tunneling. We argue that this may result in a
novel {\it ``critical Hall state''}, characterized by a power law in
tunneling experiments.Comment: 10 pages, 8 figures include
Dynamics of quantum Hall stripes in double-quantum-well systems
The collective modes of stripes in double layer quantum Hall systems are
computed using the time-dependent Hartree-Fock approximation. It is found that,
when the system possesses spontaneous interlayer coherence, there are two
gapless modes, one a phonon associated with broken translational invariance,
the other a pseudospin-wave associated with a broken U(1) symmetry. For large
layer separations the modes disperse weakly for wavevectors perpendicular to
the stripe orientation, indicating the system becomes akin to an array of
weakly coupled one-dimensional XY systems. At higher wavevectors the collective
modes develop a roton minimum associated with a transition out of the coherent
state with further increasing layer separation. A spin wave model of the system
is developed, and it is shown that the collective modes may be described as
those of a system with helimagnetic ordering.Comment: 16 pages including 7 postscript figure
Electromagnetic absorption of a pinned Wigner crystal at finite temperatures
We investigate the microwave absorption of a pinned, two-dimensional Wigner
crystal in a strong magnetic field at finite temperatures. Using a model of a
uniform commensurate pinning potential, we analyze thermal broadening of the
electromagnetic absorption resonance. Surprisingly, we find that the pinning
resonance peak should remain sharp even when the temperature is comparable or
greater than the peak frequency. This result agrees qualitatively with recent
experimental observations of the ac conductivity in two-dimensional hole
systems in a magnetically induced insulating state. It is shown, in analogy
with Kohn's theorem, that the electron-electron interaction does not affect the
response of a harmonically pinned Wigner crystal to a spatially uniform
external field at any temperature. We thus focus on anharmonicity in the
pinning potential as a source of broadening. Using a 1/N expansion technique,
we show that the broadening is introduced through the self-energy corrections
to the magnetophonon Green's functions.Comment: 21 pages, 9 eps figure
Quantum fluctuations of classical skyrmions in quantum Hall Ferromagnets
In this article, we discuss the effect of the zero point quantum fluctuations
to improve the results of the minimal field theory which has been applied to
study %SMG the skyrmions in the quantum Hall systems. Our calculation which is
based on the semiclassical treatment of the quantum fluctuations, shows that
the one-loop quantum correction provides more accurate results for the minimal
field theory.Comment: A few errors are corrected. Accepted for publication in Rapid
Communication, Phys. Rev.
Electron-Electron Interactions and the Hall-Insulator
Using the Kubo formula, we show explicitly that a non-interacting electron
system can not behave like a Hall-insulator, {\it ie.,} a DC resistivity matrix
and finite in the zero temperature
limit, as has been observed recently in experiment. For a strongly interacting
electron system in a magnetic field, we illustrate, by constructing a specific
form of correlations between mobile and localized electrons, that the Hall
resistivity can approximately equal to its classical value. A Hall-insulator is
realized in this model when the density of mobile electrons becomes vanishingly
small. It is shown that in non-interacting electron systems, the
zero-temperature frequency-dependent conductacnce generally does not give the
DC conductance.Comment: 11 pages, RevTeX3.
Statistics of skyrmions in Quantum Hall systems
We analyze statistical interactions of skyrmions in the quantum Hall system
near a critical filling fraction in the framework of the Ginzburg-Landau model.
The phase picked up by the wave-function during an exchange of two skyrmions
close to is , where is the skyrmion's
spin. In the same setting an exchange of two fully polarized vortices gives
rise to the phase . Skyrmions with odd and even numbers of reversed
spins have different quantum statistics. Condensation of skyrmions with an even
number of reversed spins leads to filling fractions with odd denominators,
while condensation of those with an odd number of reversed spins gives rise to
filling fractions with even denominators.Comment: 6 pages in Latex. addendum - skyrmions with odd or even number of
reversed spins have different quantum statistics. They condense to form
respectively even or odd denominator filling fraction state
Skyrmion Dynamics and NMR Line Shapes in QHE Ferromagnets
The low energy charged excitations in quantum Hall ferromagnets are
topological defects in the spin orientation known as skyrmions. Recent
experimental studies on nuclear magnetic resonance spectral line shapes in
quantum well heterostructures show a transition from a motionally narrowed to a
broader `frozen' line shape as the temperature is lowered at fixed filling
factor. We present a skyrmion diffusion model that describes the experimental
observations qualitatively and shows a time scale of for
the transport relaxation time of the skyrmions. The transition is characterized
by an intermediate time regime that we demonstrate is weakly sensitive to the
dynamics of the charged spin texture excitations and the sub-band electronic
wave functions within our model. We also show that the spectral line shape is
very sensitive to the nuclear polarization profile along the z-axis obtained
through the optical pumping technique.Comment: 6 pages, 4 figure
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