``Fermi Liquid'' Shell Model Approach to Composite Fermion Excitation Spectra in Fractional Quantum Hall States

Abstract

Numerical results for the energy spectra of $N$ electrons on a spherical surface are used as input data to determine the quasiparticle energies and the pairwise ``Fermi liquid'' interactions of composite Fermion (CF) excitations in fractional quantum Hall systems. The quasiparticle energies and their interactions are then used to determine the energy spectra, $E$ vs total angular momentum $L$, of states containing more than two quasiparticles. The qualitative agreement with the numerical results gives a remarkable new confirmation of the CF picture.

LaTex, 4 pages, including 4 .eps-figures, to be appear in prl

References in corpus (3)

• Band Structure of the Fractional Quantum Hall Effect
• Haldane fractional statistics in the fractional quantum Hall effect
• Excitation Spectrum and Collective Modes of Composite Fermions

Cited by in corpus (34)

• Quasiparticle Interactions in Fractional Quantum Hall Systems: Justification of Different Hierarchy Schemes
• Fractional Quantum Hall States of Clustered Composite Fermions
• State Counting for Excited Bands of the Fractional Quantum Hall Effect: Exclusion Rules for Bound Excitons
• Enigmatic 4/11 State: A Prototype for Unconventional Fractional Quantum Hall Effect
• The Composite Fermion Hierarchy: Condensed States of Composite Fermion Excitations?
• Composite Fermions and quantum Hall systems: Role of the Coulomb pseudopotential
• Possible Anti-Pfaffian Pairing of Composite Fermions in the Lowest Landau Level
• Hund's Rule for Monopole Harmonics, or Why the Composite Fermion Picture Works
• A note contrasting two microscopic theories of the fractional quantum Hall effect
• Two-Dimensional Electron-Hole Systems in a Strong Magnetic Field: Composite Fermion Picture for Multi-Component Plasmas
• Composite-fermion pairing at half and quarter filled lowest Landau level
• Abelian parton state for the $\nu =4/11$ fractional quantum Hall effect
• Composite Fermion Approach to the Quantum Hall Hierarchy: When it Works and Why
• Composite Fermions in Fractional Quantum Hall Systems
• Interacting composite fermions: Nature of the 4/5, 5/7, 6/7, and 6/17 fractional quantum Hall states
• Composite fermion pairing induced by Landau level mixing
• The Hierarchy of Incompressible Fractional Quantum Hall States
• Possible realization of a chiral p-wave paired state in a two component system
• Particle-hole symmetry for composite fermions: An emergent symmetry in the fractional quantum Hall effect
• Exclusion statistics for fractional quantum Hall states on a sphere
• Parton wave function for the fractional quantum Hall effect at $\nu =6/17$
• Static and Dynamic Properties of Type-II Composite Fermion Wigner Crystals
• Nature of the anomalous $4/13$ fractional quantum Hall effect in graphene
• Bardeen-Cooper-Schrieffer pairing of composite fermions
• Pair-distribution functions of correlated composite fermions
• Novel Families of Fractional Quantum Hall States: Pairing of Composite Fermions
• Effective mass staircase and the Fermi liquid parameters for the fractional quantum Hall composite fermions
• Integral and fractional Quantum Hall Ising ferromagnets
• A Particle-Hole-Symmetric Model for a Paired Fractional Quantum Hall State in a Half-filled Landau Level
• Unconventional Filling Factor 4/11: A Closed-Form Ground State Wave Function
• Composite fermions in the neighborhood of $\nu =1/3$
• Numerical demonstration of Abelian fractional statistics of composite fermions in the spherical geometry
• Residual interactions and correlations among Laughlin quasiparticles: Novel hierarchy states
• Electron-Hole Systems in Narrow Quantum Wells: Excitonic Complexes and Photoluminescence