Hamiltonian Description of Composite Fermions: Magnetoexciton Dispersions

Abstract

A microscopic Hamiltonian theory of the FQHE, developed by Shankar and myself based on the fermionic Chern-Simons approach, has recently been quite successful in calculating gaps in Fractional Quantum Hall states, and in predicting approximate scaling relations between the gaps of different fractions. I now apply this formalism towards computing magnetoexciton dispersions (including spin-flip dispersions) in the $\nu =1/3$, 2/5, and 3/7 gapped fractions, and find approximate agreement with numerical results. I also analyse the evolution of these dispersions with increasing sample thickness, modelled by a potential soft at high momenta. New results are obtained for instabilities as a function of thickness for 2/5 and 3/7, and it is shown that the spin-polarized 2/5 state, in contrast to the spin-polarized 1/3 state, cannot be described as a simple quantum ferromagnet.

18 pages, 18 encapsulated ps figures

References in corpus (7)

• Lowest-Landau-level theory of the quantum Hall effect: the Fermi-liquid-like state
• Towards a field theory of the fractional quantum Hall states
• A dipole interpretation of the $\nu =1/2$ state
• Quantum Hall Fluids on the Haldane Sphere: A Diffusion Monte Carlo Study
• 1/N expansion for two-dimensional quantum ferromagnets
• Hamiltonian Description of Composite Fermions: Calculation of Gaps
• Scaling Relations for Gaps in Fractional Quantum Hall States

Cited by in corpus (18)

• Spontaneous polarization of composite fermions in the $n=1$ Landau level of graphene
• Evidence of Landau levels and interactions in low-lying excitations of composite fermions at 1/3 <= ν<= 2/5
• Exact results for model wave functions of anisotropic composite fermions in the fractional quantum Hall effect
• Study of Low Energy Spin Rotons in the Fractional Quantum Hall Effect
• A note contrasting two microscopic theories of the fractional quantum Hall effect
• Transition from Free to Interacting Composite Fermions away from $\nu$=1/3
• Neutral Collective Modes in Spin-Polarized Fractional Quantum Hall States at Filling Factors 1/3, 2/5, 3/7, and 4/9
• Transport gap in a nu=1/3 quantum Hall system: a probe for skyrmions
• Light scattering observations of spin reversal excitations in the fractional quantum Hall regime
• Hamiltonian theory of the half-filled Landau level with disorder: Application to recent NMR data
• Hamiltonian theory for Quantum Hall systems in a tilted magnetic field: robustness of activation gaps
• Finite Temperature Magnetism in Fractional Quantum Hall Systems: Composite Fermion Hartree-Fock and Beyond
• Hamiltonian Theory of Disorder at 1/3
• Quantitative theory of composite fermions in Bose-Fermi mixtures at $\nu =1$
• Collective excitations of quantum Hall states under tilted magnetic field
• Spinless and spinful charge excitations in moiré Fractional Chern Insulators
• Light Scattering by Low Lying Quasiparticle Excitations in the Fractional Quantum Hall Regime
• Dipoles and fractional quantum Hall masses