2,659 research outputs found
Hund's Rule for Monopole Harmonics, or Why the Composite Fermion Picture Works
The success of the mean field composite Fermion (MFCF) picture in predicting
the lowest energy band of angular momentum multiplets in fractional quantum
Hall systems cannot be found in a cancellation between the Coulomb and
Chern--Simons interactions beyond the mean field, due to their totally
different energy scales. We show that the MFCF approximation can be regarded as
a kind of semi-empirical Hund's rule for monopole harmonics. The plausibility
of the rule is easily established, but rigorous proof relies on comparison with
detailed numerical calculations.Comment: RevTeX + 3 EPS figures formatted in the text with epsf.st
Composite Fermion Approach to the Quantum Hall Hierarchy: When it Works and Why
The mean field composite Fermion (MFCF) picture has been qualitatively
successful when applied to electrons (or holes) in the lowest Landau level.
Because the energy scales associated with Coulomb interactions and with
Chern-Simons gauge field interactions are different, there is no rigorous
justification of the qualitative success of the MFCF picture. Here we show that
what the MFCF picture does is to select from all the allowed angular momentum
(L) multiplets of N electrons on a sphere, a subset with smaller values of L.
For this subset, the coefficients of fractional parentage for pair states with
small relative angular momentum (and therefore large repulsion) either
vanish or they are small. This set of states forms the lowest energy sector of
the spectrum.Comment: RevTeX + 3 EPS figures formatted into the text with epsf.sty to
appear in Solid State Communication
Composite Fermions and the Fractional Quantum Hall Effect
The mean field (MF) composite Fermion (CF) picture successfully predicts low
lying states of fractional quantum Hall systems. This success cannot be
attributed to a cancellation between Coulomb and Chern-Simons interactions
beyond the mean field and solely depends on the short range (SR) of the Coulomb
pseudopotential in the lowest Landau level (LL). The class of pseudopotentials
for which the MFCF picture can be applied is defined. The success or failure of
the MFCF picture in various systems (electrons in excited LL's, Laughlin
quasiparticles, charged magneto-excitons) is explained.Comment: 10 pages + 4 figures (RevTeX+epsf.sty); submitted to Acta Phys. Pol.
Excitations of the Fractional Quantum Hall State and the Generalized Composite Fermion Picture
We present a generalization of the composite Fermion picture for a
muticomponent quantum Hall plasma which contains particle with different
effective charges. The model predicts very well the low-lying states of a
quantum Hall state found in numerical diagonalization.Comment: 5 pages, 3 figure
Charged Excitons in a Dilute 2D Electron Gas in a High Magnetic Field
A theory of charged excitons X- in a dilute 2D electron gas in a high
magnetic field is presented. In contrast to previous calculations, three bound
X- states (one singlet and two triplets) are found in a narrow and symmetric
GaAs quantum well. The singlet and a "bright" triplet are the two optically
active states observed in experiments. The bright triplet has the binding
energy of about 1 meV, smaller than the singlet and a "dark" triplet. The
interaction of bound X-'s with a dilute 2D electron gas is investigated using
exact diagonalization techniques. It is found that the short-range character of
the e:X- interactions effectively isolates bound X- states from a dilute e-h
plasma. This results in the insensitivity of the photoluminescence spectrum to
the filling factor nu, and an exponential decrease of the oscillator strength
of the dark triplet X- as a function of 1/nu$.Comment: 8 pages, 5 figures, submitted to Phys.Rev.
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