108 research outputs found
Fractional Quantum Hall States of Clustered Composite Fermions
The energy spectra and wavefunctions of up to 14 interacting quasielectrons
(QE's) in the Laughlin nu=1/3 fractional quantum Hall (FQH) state are
investigated using exact numerical diagonalization. It is shown that at
sufficiently high density the QE's form pairs or larger clusters. This
behavior, opposite to Laughlin correlations, invalidates the (sometimes
invoked) reapplication of the composite fermion picture to the individual QE's.
The series of finite-size incompressible ground states are identified at the QE
filling factors nu_QE=1/2, 1/3, 2/3, corresponding to the electron fillings
nu=3/8, 4/11, 5/13. The equivalent quasihole (QH) states occur at nu_QH=1/4,
1/5, 2/7, corresponding to nu=3/10, 4/13, 5/17. All these six novel FQH states
were recently discovered experimentally. Detailed analysis indicates that QE or
QH correlations in these states are different from those of well-known FQH
electron states (e.g., Laughlin or Moore-Read states), leaving the origin of
their incompressibility uncertain. Halperin's idea of Laughlin states of QP
pairs is also explored, but is does not seem adequate.Comment: 14 pages, 9 figures; revision: 1 new figure, some new references,
some new data, title chang
Fermion Chern Simons Theory of Hierarchical Fractional Quantum Hall States
We present an effective Chern-Simons theory for the bulk fully polarized
fractional quantum Hall (FQH) hierarchical states constructed as daughters of
general states of the Jain series, {\it i. e.} as FQH states of the
quasi-particles or quasi-holes of Jain states. We discuss the stability of
these new states and present two reasonable stability criteria. We discuss the
theory of their edge states which follows naturally from this bulk theory. We
construct the operators that create elementary excitations, and discuss the
scaling behavior of the tunneling conductance in different situations. Under
the assumption that the edge states of these fully polarized hierarchical
states are unreconstructed and unresolved, we find that the differential
conductance for tunneling of electrons from a Fermi liquid into {\em any}
hierarchical Jain FQH states has the scaling behavior with the
universal exponent , where is the filling fraction of the
hierarchical state. Finally, we explore alternative ways of constructing FQH
states with the same filling fractions as partially polarized states, and
conclude that this is not possible within our approach.Comment: 10 pages, 50 references, no figures; formerly known as "Composite
Fermions: The Next Generation(s)" (title changed by the PRB thought police).
This version has more references and a discussion of the stability of the new
states. Published version. One erroneous reference is correcte
Random Field Models for Relaxor Ferroelectric Behavior
Heat bath Monte Carlo simulations have been used to study a four-state clock
model with a type of random field on simple cubic lattices. The model has the
standard nonrandom two-spin exchange term with coupling energy and a random
field which consists of adding an energy to one of the four spin states,
chosen randomly at each site. This Ashkin-Teller-like model does not separate;
the two random-field Ising model components are coupled. When , the
ground states of the model remain fully aligned. When , a
different type of ground state is found, in which the occupation of two of the
four spin states is close to 50%, and the other two are nearly absent. This
means that one of the Ising components is almost completely ordered, while the
other one has only short-range correlations. A large peak in the structure
factor appears at small for temperatures well above the transition
to long-range order, and the appearance of this peak is associated with slow,
"glassy" dynamics. The phase transition into the state where one Ising
component is long-range ordered appears to be first order, but the latent heat
is very small.Comment: 7 pages + 12 eps figures, to appear in Phys Rev
Fractional-quantum-Hall edge electrons and Fermi statistics
We address the quantum statistics of electrons created in the low-energy
edge-state Hilbert space sector of incompressible fractional quantum Hall
states, considering the possibility that they may not satisfy Fermi statistics.
We argue that this property is not a priori obvious, and present numerical
evidence based on finite-size exact-diagonalization calculations that it does
not hold in general. We discuss different possible forms for the expression for
the electron creation operator in terms of edge boson fields and show that none
are consistent with our numerical results on finite-size filling-factor-2/5
states with short-range electron-electron interactions. Finally, we discuss the
current body of experimental results on tunneling into quantum Hall edges in
the context of this result.Comment: 9 pages, 1 figure, RevTex
Momentum-Resolved Tunneling into Fractional Quantum Hall Edges
Tunneling from a two-dimensional contact into quantum-Hall edges is
considered theoretically for a case where the barrier is extended, uniform, and
parallel to the edge. In contrast to previously realized tunneling geometries,
details of the microscopic edge structure are exhibited directly in the voltage
and magnetic-field dependence of the differential tunneling conductance. In
particular, it is possible to measure the dispersion of the edge-magnetoplasmon
mode, and the existence of additional, sometimes counterpropagating,
edge-excitation branches could be detected.Comment: 4 pages, 3 figures, RevTex
Energy, interaction, and photoluminescence of spin-reversed quasielectrons in fractional quantum Hall systems
The energy and photoluminescence spectra of a two-dimensional electron gas in
the fractional quantum Hall regime are studied. The single-particle properties
of reversed-spin quasielectrons (QE's) as well as the
pseudopotentials of their interaction with one another and with Laughlin
quasielectrons (QE's) and quasiholes (QH's) are calculated. Based on the
short-range character of the QE--QE and QE--QE
repulsion, the partially unpolarized incompressible states at the filling
factors and are postulated within Haldane's
hierarchy scheme. To describe photoluminescence, the family of bound
QE states of a valence hole and QE's are
predicted in analogy to the found earlier fractionally charged excitons
QE. The binding energy and optical selection rules for both families are
compared. The QE is found radiative in contrast to the dark QE,
and the QE is found non-radiative in contrast to the bright
QE.Comment: 9 pages, 6 figure
Topological Defects and Non-homogeneous Melting of Large 2D Coulomb Clusters
The configurational and melting properties of large two-dimensional clusters
of charged classical particles interacting with each other via the Coulomb
potential are investigated through the Monte Carlo simulation technique. The
particles are confined by a harmonic potential. For a large number of particles
in the cluster (N>150) the configuration is determined by two competing
effects, namely in the center a hexagonal lattice is formed, which is the
groundstate for an infinite 2D system, and the confinement which imposes its
circular symmetry on the outer edge. As a result a hexagonal Wigner lattice is
formed in the central area while at the border of the cluster the particles are
arranged in rings. In the transition region defects appear as dislocations and
disclinations at the six corners of the hexagonal-shaped inner domain. Many
different arrangements and type of defects are possible as metastable
configurations with a slightly higher energy. The particles motion is found to
be strongly related to the topological structure. Our results clearly show that
the melting of the clusters starts near the geometry induced defects, and that
three different melting temperatures can be defined corresponding to the
melting of different regions in the cluster.Comment: 7 pages, 11 figures, submitted to Phys. Rev.
Edge reconstruction in the fractional quantum Hall regime
The interplay of electron-electron interaction and confining potential can
lead to the reconstruction of fractional quantum Hall edges. We have performed
exact diagonalization studies on microscopic models of fractional quantum Hall
liquids, in finite size systems with disk geometry, and found numerical
evidence of edge reconstruction under rather general conditions. In the present
work we have taken into account effects like layer thickness and Landau level
mixing, which are found to be of quantitative importance in edge physics. Due
to edge reconstruction, additional nonchiral edge modes arise for both
incompressible and compressible states. These additional modes couple to
electromagnetic fields and thus can be detected in microwave conductivity
measurements. They are also expected to affect the exponent of electron Green's
function, which has been measured in tunneling experiments. We have studied in
this work the electric dipole spectral function that is directly related to the
microwave conductivity measurement. Our results are consistent with the
enhanced microwave conductivity observed in experiments performed on samples
with an array of antidots at low temperatures, and its suppression at higher
temperatures. We also discuss the effects of the edge reconstruction on the
single electron spectral function at the edge.Comment: 19 pages, 12 figure
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
Vortex dynamics for two-dimensional XY models
Two-dimensional XY models with resistively shunted junction (RSJ) dynamics
and time dependent Ginzburg-Landau (TDGL) dynamics are simulated and it is
verified that the vortex response is well described by the Minnhagen
phenomenology for both types of dynamics. Evidence is presented supporting that
the dynamical critical exponent in the low-temperature phase is given by
the scaling prediction (expressed in terms of the Coulomb gas temperature
and the vortex renormalization given by the dielectric constant
) both for RSJ and TDGL
and that the nonlinear IV exponent a is given by a=z+1 in the low-temperature
phase. The results are discussed and compared with the results of other recent
papers and the importance of the boundary conditions is emphasized.Comment: 21 pages including 15 figures, final versio
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