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

Abstract

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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References in corpus (2)

• ``Fermi Liquid'' Shell Model Approach to Composite Fermion Excitation Spectra in Fractional Quantum Hall States
• The Composite Fermion Hierarchy: Condensed States of Composite Fermion Excitations?

Cited by in corpus (17)

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• Quasiparticle Interactions in Fractional Quantum Hall Systems: Justification of Different Hierarchy Schemes
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• Excitonic Ions and Pseudopotentials in 2D Systems: Evidence for Quantum Hall States of an X- Gas
• Composite Fermions and the Fractional Quantum Hall Effect: Essential Role of the Pseudopotential
• Hund's Rule for Monopole Harmonics, or Why the Composite Fermion Picture Works
• Energy spectra of fractional quantum Hall systems in the presence of a valence hole
• Photoluminescence from fractional quantum Hall systems: Role of separation between electron and hole layers
• Two-Dimensional Electron-Hole Systems in a Strong Magnetic Field: Composite Fermion Picture for Multi-Component Plasmas
• Emergence of Jack ground states from two-body pseudopotentials in fractional quantum Hall systems
• Composite Fermions in Fractional Quantum Hall Systems
• The Hierarchy of Incompressible Fractional Quantum Hall States
• Energy spectra and photoluminescence of charged magneto-excitons
• Fractional quantum Hall effect and electron correlations in partially filled first excited Landau level
• Transformation of Statistics in Fractional Quantum Hall Systems
• Excitations of the $\nu =5/2$ Fractional Quantum Hall State and the Generalized Composite Fermion Picture
• Composite Fermion Picture for Multi-Component Plasmas in 2D Electron-Hole Systems in a Strong Magnetic Field