Composite Fermions and quantum Hall systems: Role of the Coulomb pseudopotential

Abstract

The mean field composite Fermion (CF) picture successfully predicts angular momenta of multiplets forming the lowest energy band in fractional quantum Hall (FQH) systems. This success cannot be attributed to a cancellation between Coulomb and Chern-Simons interactions beyond the mean field, because these interactions have totally different energy scales. Rather, it results from the behavior of the Coulomb pseudopotential V(L) (pair energy as a function of pair angular momentum) in the lowest Landau level (LL). The class of short range repulsive pseudopotentials is defined that lead to short range Laughlin like correlations in many body systems and to which the CF model can be applied. These Laughlin correlations are described quantitatively using the formalism of fractional parentage. The discussion is illustrated with an analysis of the energy spectra obtained in numerical diagonalization of up to eleven electrons in the lowest and excited LL's. The qualitative difference in the behavior of V(L) is shown to sometimes invalidate the mean field CF picture when applied to higher LL's. For example, the nu=7/3 state is not a Laughlin nu=1/3 state in the first excited LL. The analysis of the involved pseudopotentials also explains the success or failure of the CF picture when applied to other systems of charged Fermions with Coulomb repulsion, such as the Laughlin quasiparticles in the FQH hierarchy or charged excitons in an electron-hole plasma.

27 pages, 23 figures, revised version (significant changes in text and figures), submitted to Phil. Mag. B

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Cited by in corpus (29)

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• Spin excitation spectra of integral and fractional quantum Hall systems
• 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
• Emergence of Jack ground states from two-body pseudopotentials in fractional quantum Hall systems
• The Hierarchy of Incompressible Fractional Quantum Hall States
• Second Generation of Moore-Read Quasiholes in a Composite Fermion Liquid
• Three-body correlations and finite-size effects in the Moore--Read states on a sphere
• Energy, interaction, and photoluminescence of spin-reversed quasielectrons in fractional quantum Hall systems
• Pair-distribution functions of correlated composite fermions
• Novel Families of Fractional Quantum Hall States: Pairing of Composite Fermions
• Flavor altering excitations of composite fermions
• Electron correlations in a partially filled first excited Landau level
• Spin instabilities and quantum phase transitions in integral and fractional quantum Hall states
• Integral and fractional Quantum Hall Ising ferromagnets
• Fermions out of Dipolar Bosons in the lowest Landau level
• The Fermion-Boson Transformation in Fractional Quantum Hall Systems
• Skyrmions in integral and fractional quantum Hall systems
• Interaction and dynamical binding of spin waves or excitons in quantum Hall systems
• Interaction and Particle-Hole Symmetry of Laughlin Quasiparticles
• Fractionally charged magneto-excitons
• Photoluminescence of the incompressible Laughlin liquid: Excitons, charged excitons, and fractionally charged excitons
• Transformation of Statistics in Fractional Quantum Hall Systems
• Spin in fractional quantum Hall systems
• Nuclear spin relaxation in integral and fractional quantum Hall systems
• Residual interactions and correlations among Laughlin quasiparticles: Novel hierarchy states
• Reversed-Spin Quasiparticles in Fractional Quantum Hall Systems and Their Effect on Photoluminescence
• Effective mass of the composite fermions and energy gaps of quantum Hall states