10 research outputs found
Magnetoroton instabilities and static susceptibilities in higher Landau levels
We present analytical results concerning the magneto-roton instability in
higher Landau levels evaluated in the single mode approximation. The roton gap
appears at a finite wave vector, which is approximately independent of the LL
index n, in agreement with numerical calculations in the composite-fermion
picture. However, a large maximum in the static susceptibility indicates a
charge density modulation with wave vectors , as
expected from Hartree-Fock predictions. We thus obtain a unified description of
the leading charge instabilities in all LLs.Comment: 4 pages, 5 figure
Skyrmions in the Fractional Quantum Hall Effect
It is verified that, at small Zeeman energies, the charged excitations in the
vicinity of 1/3 filled Landau level are skyrmions of composite fermions,
analogous to the skyrmions of electrons near filling factor unity. These are
found to be relevant, however, only at very low magnetic fields.Comment: 13 pages including 2 postscript figures; accepted for publication in
Solid State Communications (1996
Wigner Crystals in the lowest Landau level at low filling factors
We report on results of finite-size numerical studies of partially filled
lowest Landau level at low electron filling factors. We find convincing
evidence suggesting that electrons form Wigner Crystals at sufficiently low
filling factors, and the critical filling factor is close to 1/7. At nu=1/7 we
find the system undergoes a phase transition from Wigner Crystal to the
incompressible Laughlin state when the short-range part of the Coulomb
interaction is modified slightly. This transition is either continuous or very
weakly first order.Comment: 5 papges RevTex with 8 eps figures embedded in the tex
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
Hamiltonian Description of Composite Fermions: Magnetoexciton Dispersions
A microscopic Hamiltonian theory of the FQHE, developed by Shankar and myself
based on the fermionic Chern-Simons approach, has recently been quite
successful in calculating gaps in Fractional Quantum Hall states, and in
predicting approximate scaling relations between the gaps of different
fractions. I now apply this formalism towards computing magnetoexciton
dispersions (including spin-flip dispersions) in the , 2/5, and 3/7
gapped fractions, and find approximate agreement with numerical results. I also
analyse the evolution of these dispersions with increasing sample thickness,
modelled by a potential soft at high momenta. New results are obtained for
instabilities as a function of thickness for 2/5 and 3/7, and it is shown that
the spin-polarized 2/5 state, in contrast to the spin-polarized 1/3 state,
cannot be described as a simple quantum ferromagnet.Comment: 18 pages, 18 encapsulated ps figure
Hamiltonian Theory of the FQHE: Conserving Approximation for Incompressible Fractions
A microscopic Hamiltonian theory of the FQHE developed by Shankar and the
present author based on the fermionic Chern-Simons approach has recently been
quite successful in calculating gaps and finite tempertature properties in
Fractional Quantum Hall states. Initially proposed as a small- theory, it
was subsequently extended by Shankar to form an algebraically consistent theory
for all in the lowest Landau level. Such a theory is amenable to a
conserving approximation in which the constraints have vanishing correlators
and decouple from physical response functions. Properties of the incompressible
fractions are explored in this conserving approximation, including the
magnetoexciton dispersions and the evolution of the small- structure factor
as \nu\to\half. Finally, a formalism capable of dealing with a nonuniform
ground state charge density is developed and used to show how the correct
fractional value of the quasiparticle charge emerges from the theory.Comment: 15 pages, 2 eps figure
Mixed States of Composite Fermions Carrying Two and Four Vortices
There now exists preliminary experimental evidence for some fractions, such
as = 4/11 and 5/13, that do not belong to any of the sequences
, and being integers. We propose that these states
are mixed states of composite fermions of different flavors, for example,
composite fermions carrying two and four vortices. We also obtain an estimate
of the lowest-excitation dispersion curve as well as the transport gap; the
gaps for 4/11 are smaller than those for 1/3 by approximately a factor of 50.Comment: Accepted for PRB rapid communication (scheduled to appear in Nov 15,
2000 issue
Structures for Interacting Composite Fermions: Stripes, Bubbles, and Fractional Quantum Hall Effect
Much of the present day qualitative phenomenology of the fractional quantum
Hall effect can be understood by neglecting the interactions between composite
fermions altogether. For example the fractional quantum Hall effect at
corresponds to filled composite-fermion Landau levels,and
the compressible state at to the Fermi sea of composite fermions.
Away from these filling factors, the residual interactions between composite
fermions will determine the nature of the ground state. In this article, a
model is constructed for the residual interaction between composite fermions,
and various possible states are considered in a variational approach. Our study
suggests formation of composite-fermion stripes, bubble crystals, as well as
fractional quantum Hall states for appropriate situations.Comment: 16 pages, 7 figure
Positions of the magnetoroton minima in the fractional quantum Hall effect
The multitude of excitations of the fractional quantum Hall state are very
accurately understood, microscopically, as excitations of composite fermions
across their Landau-like levels. In particular, the dispersion of the
composite fermion exciton, which is the lowest energy spin conserving neutral
excitation, displays filling-factor-specific minima called "magnetoroton"
minima. Simon and Halperin employed the Chern-Simons field theory of composite
fermions [Phys. Rev. B {\bf 48}, 17368 (1993)] to predict the magnetoroton
minima positions. Recently, Golkar \emph{et al.} [Phys. Rev. Lett. {\bf 117},
216403 (2016)] have modeled the neutral excitations as deformations of the
composite fermion Fermi sea, which results in a prediction for the positions of
the magnetoroton minima. Using methods of the microscopic composite fermion
theory we calculate the positions of the roton minima for filling factors up to
5/11 along the sequence and find them to be in reasonably good
agreement with both the Chern-Simons field theory of composite fermions and
Golkar \emph{et al.}'s theory. We also find that the positions of the roton
minima are insensitive to the microscopic interaction in agreement with Golkar
\emph{et al.}'s theory. As a byproduct of our calculations, we obtain the
charge and neutral gaps for the fully spin polarized states along the sequence
in the lowest Landau level and the Landau level of
graphene.Comment: 9 pages, 5 figures, published versio