609 research outputs found
Current and charge distributions of the fractional quantum Hall liquids with edges
An effective Chern-Simons theory for the quantum Hall states with edges is
studied by treating the edge and bulk properties in a unified fashion. An exact
steady-state solution is obtained for a half-plane geometry using the
Wiener-Hopf method. For a Hall bar with finite width, it is proved that the
charge and current distributions do not have a diverging singularity. It is
shown that there exists only a single mode even for the hierarchical states,
and the mode is not localized exponentially near the edges. Thus this result
differs from the edge picture in which electrons are treated as strictly one
dimensional chiral Luttinger liquids.Comment: 21 pages, REV TeX fil
Universal structure of the edge states of the fractional quantum Hall states
We present an effective theory for the bulk fractional quantum Hall states on
the Jain sequences on closed surfaces and show that it has a universal form
whose structure does not change from fraction to fraction. The structure of
this effective theory follows from the condition of global consistency of the
flux attachment transformation on closed surfaces. We derive the theory of the
edge states on a disk that follows naturally from this globally consistent
theory on a torus. We find that, for a fully polarized two-dimensional electron
gas, the edge states for all the Jain filling fractions have
only one propagating edge field that carries both energy and charge, and two
non-propagating edge fields of topological origin that are responsible for the
statistics of the excitations. Explicit results are derived for the electron
and quasiparticle operators and for their propagators at the edge. We show that
these operators create states with the correct charge and statistics. It is
found that the tunneling density of states for all the Jain states scales with
frequency as .Comment: 10 page
How universal is the fractional-quantum-Hall edge Luttinger liquid?
This article reports on our microscopic investigations of the edge of the
fractional quantum Hall state at filling factor . We show that the
interaction dependence of the wave function is well described in an
approximation that includes mixing with higher composite-fermion Landau levels
in the lowest order. We then proceed to calculate the equal time edge Green
function, which provides evidence that the Luttinger exponent characterizing
the decay of the Green function at long distances is interaction dependent. The
relevance of this result to tunneling experiments is discussed.Comment: 5 page
Quantum Transport in Two-Channel Fractional Quantum Hall Edges
We study the effect of backward scatterings in the tunneling at a point
contact between the edges of a second level hierarchical fractional quantum
Hall states. A universal scaling dimension of the tunneling conductance is
obtained only when both of the edge channels propagate in the same direction.
It is shown that the quasiparticle tunneling picture and the electron tunneling
picture give different scaling behaviors of the conductances, which indicates
the existence of a crossover between the two pictures. When the direction of
two edge-channels are opposite, e.g. in the case of MacDonald's edge
construction for the state, the phase diagram is divided into two
domains giving different temperature dependence of the conductance.Comment: 21 pages (REVTeX and 1 Postscript figure
Edge excitations and Topological orders in rotating Bose gases
The edge excitations and related topological orders of correlated states of a
fast rotating Bose gas are studied. Using exact diagonalization of small
systems, we compute the energies and number of edge excitations, as well as the
boson occupancy near the edge for various states. The chiral Luttinger-liquid
theory of Wen is found to be a good description of the edges of the bosonic
Laughlin and other states identified as members of the principal Jain sequence
for bosons. However, we find that in a harmonic trap the edge of the state
identified as the Moore-Read (Pfaffian) state shows a number of anomalies. An
experimental way of detecting these correlated states is also discussed.Comment: Results extended to larger systems. Improved presentatio
Characterization of fractional-quantum-Hall-effect quasiparticles
Composite fermions in a partially filled quasi-Landau level may be viewed as
quasielectrons of the underlying fractional quantum Hall state, suggesting that
a quasielectron is simply a dressed electron, as often is true in other
interacting electron systems, and as a result has the same intrinsic charge and
exchange statistics as an electron. This paper discusses how this result is
reconciled with the earlier picture in which quasiparticles are viewed as
fractionally-charged fractional-statistics ``solitons". While the two
approaches provide the same answers for the long-range interactions between the
quasiparticles, the dressed-electron description is more conventional and
unifies the view of quasiparticle dynamics in and beyond the fractional quantum
Hall regime.Comment: 11 pages, latex, no figure
Invariance of Charge of Laughlin Quasiparticles
A Quantum Antidot electrometer has been used in the first direct observation
of the fractionally quantized electric charge. In this paper we report
experiments performed on the integer i = 1, 2 and fractional f = 1/3 quantum
Hall plateaus extending over a filling factor range of at least 27%. We find
the charge of the Laughlin quasiparticles to be invariantly e/3, with standard
deviation of 1.2% and absolute accuracy of 4%, independent of filling,
tunneling current, and temperature.Comment: 4 pages, 5 fig
Edge and Bulk of the Fractional Quantum Hall Liquids
An effective Chern-Simons theory for the Abelian quantum Hall states with
edges is proposed to study the edge and bulk properties in a unified fashion.
We impose a condition that the currents do not flow outside the sample. With
this boundary condition, the action remains gauge invariant and the edge modes
are naturally derived. We find that the integer coupling matrix should
satisfy the condition (: filling of Landau
levels, : the number of gauge fields ) for the quantum Hall liquids. Then
the Hall conductance is always quantized irrespective of the detailed dynamics
or the randomness at the edge.Comment: 13 pages, REVTEX, one figure appended as a postscript fil
Impurity scattering and transport of fractional Quantum Hall edge state
We study the effects of impurity scattering on the low energy edge state
dynamic s for a broad class of quantum Hall fluids at filling factor , for integer and even integer . When is positive all
of the edge modes are expected to move in the same direction, whereas for
negative one mode moves in a direction opposite to the other modes.
Using a chiral-Luttinger model to describe the edge channels, we show that for
an ideal edge when is negative, a non-quantized and non-universal Hall
conductance is predicted. The non-quantized conductance is associated with an
absence of equilibration between the edge channels. To explain the robust
experimental Hall quantization, it is thus necessary to incorporate impurity
scattering into the model, to allow for edge equilibration. A perturbative
analysis reveals that edge impurity scattering is relevant and will modify the
low energy edge dynamics. We describe a non-perturbative solution for the
random channel edge, which reveals the existence of a new
disorder-dominated phase, characterized by a stable zero temperature
renormalization group fixed point. The phase consists of a single propagating
charge mode, which gives a quantized Hall conductance, and neutral modes.
The neutral modes all propagate at the same speed, and manifest an exact SU(n)
symmetry. At finite temperatures the SU(n) symmetry is broken and the neutral
modes decay with a finite rate which varies as at low temperatures.
Various experimental predictions and implications which follow from the exact
solution are described in detail, focusing on tunneling experiments through
point contacts.Comment: 19 pages (two column), 5 post script figures appended, 3.0 REVTE
Edge reconstructions in fractional quantum Hall systems
Two dimensional electron systems exhibiting the fractional quantum Hall
effects are characterized by a quantized Hall conductance and a dissipationless
bulk. The transport in these systems occurs only at the edges where gapless
excitations are present. We present a {\it microscopic} calculation of the edge
states in the fractional quantum Hall systems at various filling factors using
the extended Hamiltonian theory of the fractional quantum Hall effect. We find
that at the quantum Hall edge undergoes a reconstruction as the
background potential softens, whereas quantum Hall edges at higher filling
factors, such as , are robust against reconstruction. We present
the results for the dependence of the edge states on various system parameters
such as temperature, functional form and range of electron-electron
interactions, and the confining potential. Our results have implications for
the tunneling experiments into the edge of a fractional quantum Hall system.Comment: 11 pages, 9 figures; minor typos corrected; added 2 reference
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