24 research outputs found
Various spin-polarization states beyond the maximum-density droplet: a quantum Monte Carlo study
Using variational quantum Monte Carlo method, the effect of Landau-level
mixing on the lowest-energy--state diagram of small quantum dots is studied in
the magnetic field range where the density of magnetic flux quanta just exceeds
the density of electrons. An accurate analytical many-body wave function is
constructed for various angular momentum and spin states in the lowest Landau
level, and Landau-level mixing is then introduced using a Jastrow factor. The
effect of higher Landau levels is shown to be significant; the transition lines
are shifted considerably towards higher values of magnetic field and certain
lowest-energy states vanish altogether.Comment: 4 pages, 2 figures. Submitted to Phys. Rev.
Partially spin polarized quantum Hall effect in the filling factor range 1/3 < nu < 2/5
The residual interaction between composite fermions (CFs) can express itself
through higher order fractional Hall effect. With the help of diagonalization
in a truncated composite fermion basis of low-energy many-body states, we
predict that quantum Hall effect with partial spin polarization is possible at
several fractions between and . The estimated excitation
gaps are approximately two orders of magnitude smaller than the gap at
, confirming that the inter-CF interaction is extremely weak in higher
CF levels.Comment: 4 pages, 3 figure
Algebraic Quantization, Good Operators and Fractional Quantum Numbers
The problems arising when quantizing systems with periodic boundary
conditions are analysed, in an algebraic (group-) quantization scheme, and the
``failure" of the Ehrenfest theorem is clarified in terms of the already
defined notion of {\it good} (and {\it bad}) operators. The analysis of
``constrained" Heisenberg-Weyl groups according to this quantization scheme
reveals the possibility for new quantum (fractional) numbers extending those
allowed for Chern classes in traditional Geometric Quantization. This study is
illustrated with the examples of the free particle on the circumference and the
charged particle in a homogeneous magnetic field on the torus, both examples
featuring ``anomalous" operators, non-equivalent quantization and the latter,
fractional quantum numbers. These provide the rationale behind flux
quantization in superconducting rings and Fractional Quantum Hall Effect,
respectively.Comment: 29 pages, latex, 1 figure included with EPSF. Revised version with
minor changes intended to clarify notation. Acepted for publication in Comm.
Math. Phy
Quantifying the levitation picture of extended states in lattice models
The behavior of extended states is quantitatively analyzed for two
dimensional lattice models. A levitation picture is established for both
white-noise and correlated disorder potentials. In a continuum limit window of
the lattice models we find simple quantitative expressions for the extended
states levitation, suggesting an underlying universal behavior. On the other
hand, these results point out that the Quantum Hall phase diagrams may be
disorder dependent.Comment: 5 pages, submitted to PR
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
The Effects of Disorder on the Quantum Hall State
A disorder-averaged Hartree-Fock treatment is used to compute the density of
single particle states for quantum Hall systems at filling factor . It
is found that transport and spin polarization experiments can be simultaneously
explained by a model of mostly short-range effective disorder. The slope of the
transport gap (due to quasiparticles) in parallel field emerges as a result of
the interplay between disorder-induced broadening and exchange, and has
implications for skyrmion localization.Comment: 4 pages, 3 eps figure
Vortex with Fractional Quantum Numbers in Chiral p-Wave Superconductor
We show that a vortex in a chiral p-wave superconductor, which has the p_{x}+
i p_{y}-wave pairing state and breaks U(1), parity and time reversal symmetry
simultaneously, has fractional charge -{n e}/{4} and fractional angular
momentum -n^{2}/{16} (n; vorticity). This suggests that the vortex could be
anyon and could obey fractional statistics. Electromagnetic property of the
vortex is also discussed and we find that an electric field is induced near the
vortex core.Comment: 10 pages, 3 figures, accepted for publication in Phys. Rev.
Weak Localization and Integer Quantum Hall Effect in a Periodic Potential
We consider magnetotransport in a disordered two-dimensional electron gas in
the presence of a periodic modulation in one direction. Existing quasiclassical
and quantum approaches to this problem account for Weiss oscillations in the
resistivity tensor at moderate magnetic fields, as well as a strong
modulation-induced modification of the Shubnikov-de Haas oscillations at higher
magnetic fields. They do not account, however, for the operation at even higher
magnetic fields of the integer quantum Hall effect, for which quantum
interference processes are responsible. We then introduce a field-theory
approach, based on a nonlinear sigma model, which encompasses naturally both
the quasiclassical and quantum-mechanical approaches, as well as providing a
consistent means of extending them to include quantum interference corrections.
A perturbative renormalization-group analysis of the field theory shows how
weak localization corrections to the conductivity tensor may be described by a
modification of the usual one-parameter scaling, such as to accommodate the
anisotropy of the bare conductivity tensor. We also show how the two-parameter
scaling, conjectured as a model for the quantum Hall effect in unmodulated
systems, may be generalized similarly for the modulated system. Within this
model we illustrate the operation of the quantum Hall effect in modulated
systems for parameters that are realistic for current experiments.Comment: 15 pages, 4 figures, ReVTeX; revised version with condensed
introduction; two figures taken out; reference adde
Dimensional Crossover of Localisation and Delocalisation in a Quantum Hall Bar
The 2-- to 1--dimensional crossover of the localisation length of electrons
confined to a disordered quantum wire of finite width is studied in a
model of electrons moving in the potential of uncorrelated impurities. An
analytical formula for the localisation length is derived, describing the
dimensional crossover as function of width , conductance and
perpendicular magnetic field . On the basis of these results, the scaling
analysis of the quantum Hall effect in high Landau levels, and the
delocalisation transition in a quantum Hall wire are reconsidered.Comment: 12 pages, 7 figure
Magnetic Field Dependence of Gate Voltage and Current in a GaAs-Heterostructure in the Quantum Hall Regime
The current flow at a fixed gate voltage and the floating gate voltage for fixed charge density in a gated GaAs heterostructure have been measured as a function of the magnetic field. The voltage oscillations which reflect the behaviour of the chemical potential have been clearly resolved. The experimental results are explained by a statistical model of inhomogeneities in the carrier concentration implying an effective density of states between the Landau levels