9 research outputs found
Quantum Hall Skyrmions with Higher Topological Charge
We have investigated quantum Hall skyrmions at filling factor \nu=1 carrying
more than one unit of topological, and hence electric, charge. Using a
combination of analytic and numerical methods we find the counterintuitive
result that when the Zeeman energy is tuned to values much smaller than the
interaction energy (g \mu_B B/(e^2/\epsilon\ell) < 9*10^{-5}),the creation
energy of a charge two skyrmion becomes less than twice the creation energy of
a charge one skyrmion, i.e. skyrmions bind in pairs. The doubly charged
skyrmions are stable to further accretion of charge and exhibit a 10% larger
spin per unit charge than charge one skyrmions which would, in principle,
signal this pairing.Comment: 4 pages, 3 figures. Submitted to Phys. Rev. B, Rapid Communication
NMR linewidth and Skyrmion localization in quantum Hall ferromagnets
The non-monotonic behavior of the NMR signal linewidth in the 2D quantum Hall
system is explained in terms of the interplay between skyrmions localization,
due to the influence of disorder, and the non-trivial temperature dependent
skyrmion dynamics.Comment: 5 pages, 2 figure
Reconstruction of the Quantum Hall Edge
The sharp \nu=1 quantum Hall edge present for hard confinement is shown to
have two modes that go soft as the confining potential softens. This signals a
second order transition to a reconstructed edge that is either a depolarized
spin-texture edge or a polarized charge density wave edge.Comment: 6 pages, 4 figures, to be published in the proceedings of the
workshop on ``Novel Physics in Low-Dimensional Electron Systems'' held in
Dresden, Physica
Bulk and edge excitations of a Hall ferromagnet
In this article, we shall focus on the collective dynamics of the fermions in
a quantum Hall droplet. Specifically, we propose to look at the
quantum Hall ferromagnet. In this system, the electron spins are ordered in the
ground state due to the exchange part of the Coulomb interaction and the Pauli
exclusion principle. The low energy excitations are ferromagnetic magnons. In
order to obtain an effective Lagrangian for these magnons, we shall introduce
bosonic collective coordinates in the Hilbert space of many-fermion systems.
These collective coordinates describe a part of the fermionic Hilbert space.
Using this technique, we shall interpret the magnons as bosonic collective
excitations in the Hilbert space of the many-electron Hall system. Furthermore,
by considering a Hall droplet of finite extent, we shall also obtain the
effective Lagrangian governing the spin collective excitations at the edge of
the sample.Comment: 30 pages, plain TeX, no figure
Spin-excitations of the quantum Hall ferromagnet of composite fermions
The spin-excitations of a fractional quantum Hall system are evaluated within
a bosonization approach. In a first step, we generalize Murthy and Shankar's
Hamiltonian theory of the fractional quantum Hall effect to the case of
composite fermions with an extra discrete degree of freedom. Here, we mainly
investigate the spin degrees of freedom, but the proposed formalism may be
useful also in the study of bilayer quantum-Hall systems, where the layer index
may formally be treated as an isospin. In a second step, we apply a
bosonization scheme, recently developed for the study of the two-dimensional
electron gas, to the interacting composite-fermion Hamiltonian. The dispersion
of the bosons, which represent quasiparticle-quasihole excitations, is
analytically evaluated for fractional quantum Hall systems at \nu = 1/3 and \nu
= 1/5. The finite width of the two-dimensional electron gas is also taken into
account explicitly. In addition, we consider the interacting bosonic model and
calculate the lowest-energy state for two bosons. Besides a continuum
describing scattering states, we find a bound-state of two bosons. This state
is interpreted as a pair excitation, which consists of a skyrmion of composite
fermions and an antiskyrmion of composite fermions. The dispersion relation of
the two-boson state is evaluated for \nu = 1/3 and \nu = 1/5. Finally, we show
that our theory provides the microscopic basis for a phenomenological
non-linear sigma-model for studying the skyrmion of composite fermions.Comment: Revised version, 14 pages, 4 figures, accepted to Phys. Rev.
Dynamics of the Compact, Ferromagnetic \nu=1 Edge
We consider the edge dynamics of a compact, fully spin polarized state at
filling factor . We show that there are two sets of collective
excitations localized near the edge: the much studied, gapless, edge
magnetoplasmon but also an additional edge spin wave that splits off below the
bulk spin wave continuum. We show that both of these excitations can soften at
finite wave-vectors as the potential confining the system is softened, thereby
leading to edge reconstruction by spin texture or charge density wave
formation. We note that a commonly employed model of the edge confining
potential is non-generic in that it systematically underestimates the texturing
instability.Comment: 13 pages, 7 figures, Revte
Effective Action Studies of Quantum Hall Spin Textures
We report on analytic and numerical studies of spin textures in quantum Hall
systems using a long-wavelength effective action for the magnetic degrees of
freedom derived previously. The majority of our results concern skyrmions or
solitons of this action. We have constructed approximate analytic solutions for
skyrmions of arbitrary topological and electric charge and derived expressions
for their energies and charge and spin radii. We describe a combined
shooting/relaxational technique for numerical determination of the skyrmion
profiles and present results that compare favorably with the analytic treatment
as well as with Hartree-Fock studies of these objects. In addition, we describe
a treatment of textures at the edges of quantum Hall systems within this
approach and provide details not reported previously.Comment: 13 pages, 10 figure