Composite Fermion Approach to the Quantum Hall Hierarchy: When it Works and Why

Details Composite Fermion Approach to the Quantum Hall Hierarchy: When it Works and Why Composite Fermion Approach to the Quantum Hall Hierarchy: When it Works and Why

1998-10-07

arxiv.org/abs/cond-mat/9810078v1

Solid State Commun. 108, 493 (1998)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

RevTeX + 3 EPS figures formatted into the text with epsf.sty to appear in Solid State Communications

Scientific paper

10.1016/S0038-1098(98)00315-9

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 $R$ (and therefore large repulsion) either vanish or they are small. This set of states forms the lowest energy sector of the spectrum.

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