59 research outputs found
The Onset of Anisotropic Transport of Two-Dimensional Electrons in High Landau Levels: An Isotropic-to-Nematic Liquid Crystal Phase Transition?
The recently discovered anisotropy of the longitudinal resistance of
two-dimensional electrons near half filling of high Landau levels is found to
persist to much higher temperatures T when a large in-plane magnetic field B||
is applied. Under these conditions we find that the longitudinal resistivity
scales quasi-linearly with B||/T. These observations support the notion that
the onset of anisotropy at B||=0 does not reflect the spontaneous development
of charge density modulations but may instead signal an isotropic-to-nematic
liquid crystal phase transition.Comment: 5 pages, 4 figure
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
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
Competition between quantum-liquid and electron-solid phases in intermediate Landau levels
On the basis of energy calculations we investigate the competition between
quantum-liquid and electron-solid phases in the Landau levels n=1,2, and 3 as a
function of their partial filling factor. Whereas the quantum-liquid phases are
stable only in the vicinity of quantized values 1/(2s+1) of the partial filling
factor, an electron solid in the form of a triangular lattice of clusters with
a few number of electrons (bubble phase) is energetically favorable between
these fillings. This alternation of electron-solid phases, which are insulating
because they are pinned by the residual impurities in the sample, and quantum
liquids displaying the fractional quantum Hall effect explains a recently
observed reentrance of the integral quantum Hall effect in the Landau levels
n=1 and 2. Around half-filling of the last Landau level, a uni-directional
charge density wave (stripe phase) has a lower energy than the bubble phase.Comment: 12 pages, 9 figures; calculation of exact exchange potential for
n=1,2,3 included, energies of electron-solid phases now calculated with the
help of the exact potential, and discussion of approximation include
Theory of the Quantum Hall Smectic Phase II: Microscopic Theory
We present a microscopic derivation of the hydrodynamic theory of the Quantum
Hall smectic or stripe phase of a two-dimensional electron gas in a large
magnetic field. The effective action of the low energy is derived here from a
microscopic picture by integrating out high energy excitations with a scale of
the order the cyclotron energy.The remaining low-energy theory can be expressed
in terms of two canonically conjugate sets of degrees of freedom: the
displacement field, that describes the fluctuations of the shapes of the
stripes, and the local charge fluctuations on each stripe.Comment: 20 pages, RevTex, 3 figures, second part of cond-mat/0105448 New and
improved Introduction. Final version as it will appear in Physical Review
Anisotropic transport in unidirectional lateral superlattice around half-filling of the second Landau level
We have observed marked transport anisotropy in short period (a=92 nm)
unidirectional lateral superlattices around filling factors nu=5/2 and 7/2:
magnetoresistance shows a sharp peak for current along the modulation grating
while a dip appears for current across the grating. By altering the ratio a/l
(with l=sqrt{hbar/eB_perp} the magnetic length) via changing the electron
density n_e, it is shown that the nu=5/2 anisotropic features appear in the
range 6.6 alt a/l alt 7.2 varying their intensities, becoming most conspicuous
at a/l simeq 6.7. The peak/dip broadens with temperature roughly preserving its
height/depth up to 250 mK. Tilt experiments reveal that the structures are
slightly enhanced by an in-plane magnetic field B_| perpendicular to the
grating but are almost completely destroyed by B_| parallel to the grating. The
observations suggest the stabilization of a unidirectional charge-density-wave
or stripe phase by weak external periodic modulation at the second Landau
level.Comment: REVTeX, 5 pages, 3 figures, Some minor revisions, Added notes and
reference
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
Quantum Hall ferromagnets, cooperative transport anisotropy, and the random field Ising model
We discuss the behaviour of a quantum Hall system when two Landau levels with
opposite spin and combined filling factor near unity are brought into energetic
coincidence using an in-plane component of magnetic field. We focus on the
interpretation of recent experiments under these conditions [Zeitler et al,
Phys. Rev. Lett. 86, 866 (2001); Pan et al, Phys. Rev. B 64, 121305 (2001)], in
which a large resistance anisotropy develops at low temperatures. Modelling the
systems involved as Ising quantum Hall ferromagnets, we suggest that this
transport anisotropy reflects domain formation induced by a random field
arising from isotropic sample surface roughness.Comment: 4 pages, submitted to Physical Review
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
Analytical approach to bit-string models of language evolution
A formulation of bit-string models of language evolution, based on
differential equations for the population speaking each language, is introduced
and preliminarily studied. Connections with replicator dynamics and diffusion
processes are pointed out. The stability of the dominance state, where most of
the population speaks a single language, is analyzed within a mean-field-like
approximation, while the homogeneous state, where the population is evenly
distributed among languages, can be exactly studied. This analysis discloses
the existence of a bistability region, where dominance coexists with
homogeneity as possible asymptotic states. Numerical resolution of the
differential system validates these findings.Comment: To appear in Int. J. Mod. Phys.
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