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Fractional quantum Hall edge: Effect of nonlinear dispersion and edge roton
According to Wen's theory, a universal behavior of the fractional quantum
Hall edge is expected at sufficiently low energies, where the dispersion of the
elementary edge excitation is linear. A microscopic calculation shows that the
actual dispersion is indeed linear at low energies, but deviates from linearity
beyond certain energy, and also exhibits an "edge roton minimum." We determine
the edge exponent from a microscopic approach, and find that the nonlinearity
of the dispersion makes a surprisingly small correction to the edge exponent
even at energies higher than the roton energy. We explain this insensitivity as
arising from the fact that the energy at maximum spectral weight continues to
show an almost linear behavior up to fairly high energies. We also formulate an
effective field theory to describe the behavior of a reconstructed edge, taking
into account multiple edge modes. Experimental consequences are discussed.Comment: 15 pages with 10 figures. Submitted to Physical Review
Dynamics of Dissipative Quantum Hall Edges
We examine the influence of the edge electronic density profile and of
dissipation on edge magnetoplasmons in the quantum Hall regime, in a
semiclassical calculation. The equilibrium electron density on the edge,
obtained using a Thomas-Fermi approach, has incompressible stripes produced by
energy gaps responsible for the quantum Hall effect. We find that these stripes
have an unobservably small effect on the edge magnetoplasmons. But dissipation,
included phenomenologically in the local conductivity, proves to produce
significant oscillations in the strength and speed of edge magnetoplasmons in
the quantum Hall regime.Comment: 23 pages including 10 figure
Bulk Versus Edge in the Quantum Hall Effect
The manifestation of the bulk quantum Hall effect on edge is the chiral
anomaly. The chiral anomaly {\it is} the underlying principle of the ``edge
approach'' of quantum Hall effect. In that approach, \sxy should not be taken
as the conductance derived from the space-local current-current correlation
function of the pure one-dimensional edge problem.Comment: 4 pages, RevTex, 1 postscript figur
Spontaneous edge currents for the Dirac equation in two space dimensions
Spontaneous edge currents are known to occur in systems of two space
dimensions in a strong magnetic field. The latter creates chirality and
determines the direction of the currents. Here we show that an analogous effect
occurs in a field-free situation when time reversal symmetry is broken by the
mass term of the Dirac equation in two space dimensions. On a half plane, one
sees explicitly that the strength of the edge current is proportional to the
difference between the chemical potentials at the edge and in the bulk, so that
the effect is analogous to the Hall effect, but with an internal potential. The
edge conductivity differs from the bulk (Hall) conductivity on the whole plane.
This results from the dependence of the edge conductivity on the choice of a
selfadjoint extension of the Dirac Hamiltonian. The invariance of the edge
conductivity with respect to small perturbations is studied in this example by
topological techniques.Comment: 10 pages; final versio
Experimental investigation of the edge states structure at fractional filling factors
We experimentally study electron transport between edge states in the
fractional quantum Hall effect regime. We find an anomalous increase of the
transport across the 2/3 incompressible fractional stripe in comparison with
theoretical predictions for the smooth edge potential profile. We interpret our
results as a first experimental demonstration of the intrinsic structure of the
incompressible stripes arising at the sample edge in the fractional quantum
Hall effect regime.Comment: 5 pages, 5 figures included. Submitted to JETP Letter
Persistent Edge Current In the Fractional Quantum Hall Effect
We study the persistent edge current in the fractional quantum Hall effect.
We give the grand partition functions for edge excitations of hierarchical
states coupled to an Aharanov-Bohm flux and derive the exact formula of the
persistent edge current. For -th hierarchical states with , it exhibits
anomalous oscillations in its flux dependence at low temperatures. The current
as a function of flux goes to the sawtooth function with period in
the zero temperature limit. This phenomenon provides a new evidence for exotic
condensation in the fractional quantum Hall effect. We propose experiments of
measuring the persistent edge current to confirm the existence of the
hierarchy.Comment: RevTex. 4 pages, 2 figure
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