25,241 research outputs found
Activation gaps for the fractional quantum Hall effect: realistic treatment of transverse thickness
The activation gaps for fractional quantum Hall states at filling fractions
are computed for heterojunction, square quantum well, as well as
parabolic quantum well geometries, using an interaction potential calculated
from a self-consistent electronic structure calculation in the local density
approximation. The finite thickness is estimated to make 30% correction
to the gap in the heterojunction geometry for typical parameters, which
accounts for roughly half of the discrepancy between the experiment and
theoretical gaps computed for a pure two dimensional system. Certain model
interactions are also considered. It is found that the activation energies
behave qualitatively differently depending on whether the interaction is of
longer or shorter range than the Coulomb interaction; there are indications
that fractional Hall states close to the Fermi sea are destabilized for the
latter.Comment: 32 pages, 13 figure
Band Structure of the Fractional Quantum Hall Effect
The eigenstates of interacting electrons in the fractional quantum Hall phase
typically form fairly well defined bands in the energy space. We show that the
composite fermion theory gives insight into the origin of these bands and
provides an accurate and complete microscopic description of the strongly
correlated many-body states in the low-energy bands. Thus, somewhat like in
Landau's fermi liquid theory, there is a one-to-one correspondence between the
low energy Hilbert space of strongly interacting electrons in the fractinal
quantum Hall regime and that of weakly interacting electrons in the integer
quantum Hall regime.Comment: 10 page
Composite fermion theory of rapidly rotating two-dimensional bosons
Ultracold neutral bosons in a rapidly rotating atomic trap have been
predicted to exhibit fractional quantum Hall-like states. We describe how the
composite fermion theory, used in the description of the fractional quantum
Hall effect for electrons, can be applied to interacting bosons. Numerical
evidence supporting the formation of composite fermions, each being the bound
state of a boson and one flux quantum, is shown for filling fractions of the
type nu=p/(p+1), both by spectral analysis and by direct comparison with trial
wave functions. The rapidly rotating system of two-dimensional bosons thus
constitutes an interesting example of "statistical transmutation," with bosons
behaving like composite fermions. We also describe the difference between the
electronic and the bosonic cases when p approaches infinity. Residual
interactions between composite fermions are attractive in this limit, resulting
in a paired composite-fermion state described by the Moore-Read wave function.Comment: 12 pages, 9 figures. Conference proceeding. BEC 2005 Ital
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