Neutral Collective Modes in Spin-Polarized Fractional Quantum Hall States at Filling Factors 1/3, 2/5, 3/7, and 4/9

Abstract

We determine the lowest and higher order collective modes in both spin-conserving and spin-reversed sectors by calculating energy differences of the appropriate linear combinations of different levels of composite-fermion-excitons and the fully spin-polarized ground states at filling factors $\nu =1/3$, 2/5, 3/7, and 4/9. Apart from providing the detailed study of previously reported modes that have also been observed in the experiments, we predict additional higher energy modes at different filling factors. The lowest and the next higher spin-conserving modes have equal number of "magneto-rotons" and the number is the same as the number of filled effective Landau-like levels of composite fermions. The higher energy modes at $\nu =1/3$ merge with the lowest mode at long-wavelength. The spin-conserving modes do not merge at other filling factors. Apart from showing zero-energy spin-wave mode at zero momentum, thanks to Larmor's theorem, the lowest spin-reversed modes at the ferromagnetic ground states of $\nu =2/5$, 3/7, and 4/9 display one or more "spin-rotons" at negative energies signalling the unstable fully polarized ground states at sufficiently small Zeeman energies. The high energy spin-reversed modes also have spin-rotons but at positive energies. The energies of these excitations depend on the finite width of the quantum well as the Coulomb interaction gets screened. We determine finite thickness correction to the Coulomb interaction by the standard method of local density approximation and use them to calculate the critical energies such as rotons, long-wavelength, and short-wavelength modes which are detectable in inelastic light scattering experiments.

arXiv comment13 pages, 15 figures

References in corpus (18)

• Composite Fermions in the Hilbert Space of the Lowest Electronic Landau Level
• Band Structure of the Fractional Quantum Hall Effect
• Theoretical Search for Nested Quantum Hall Effect of Composite Fermions
• Magneto-roton excitation of fractional quantum Hall effect: Comparison between theory and experiment
• Composite fermion theory of collective excitations in fractional quantum Hall effect
• Realistic Calculations of Correlated Incompressible Electronic States in GaAs--Al_{x}Ga_{1-x}As Heterostructures and Quantum Wells
• Splitting of Long-Wavelength Modes of the Fractional Quantum Hall Liquid at $\nu =1/3$
• Evidence of Landau levels and interactions in low-lying excitations of composite fermions at 1/3 <= ν<= 2/5
• Excitation Spectrum and Collective Modes of Composite Fermions
• Anomalous structure in the single particle spectrum of the fractional quantum Hall effect
• Activation gaps for the fractional quantum Hall effect: realistic treatment of transverse thickness
• Study of Low Energy Spin Rotons in the Fractional Quantum Hall Effect
• Higher Energy Composite Fermion Levels in the Fractional Quantum Hall Effect
• Hamiltonian Description of Composite Fermions: Magnetoexciton Dispersions
• Nature of Quasielectrons and the Continuum of Neutral Bulk Excitations in the Laughlin Quantum Hall Fluids
• Observation of non-conventional spin waves in composite fermion ferromagnets
• Girvin-MacDonald-Platzman Collective Mode at General Filling Factors: Magneto-Roton Minimum at Half-Filled Landau Level
• Testing the Landau Fermi liquid description of the fractional quantum Hall effect

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• Interplay between fractional quantum Hall liquid and crystal phases at low filling
• Strong-Magnetic-Field Magnon Transport in Monolayer Graphene
• Positions of the magnetoroton minima in the fractional quantum Hall effect
• Splitting of Girvin-MacDonald-Platzman density wave and the nature of chiral gravitons in fractional quantum Hall effect
• Roton minimum at $\nu =1/2$ filled fractional quantum Hall effect of Bose particles
• Study of partially polarized fractional quantum Hall states
• Very high-energy collective states of partons in fractional quantum Hall liquids
• Double roton-minima in bosonic fractional quantum Hall states
• Hydrodynamic study of edge spin-vortex excitations of fractional quantum Hall fluid
• Dispersion of collective modes in spinful fractional quantum Hall states on the sphere