Girvin-MacDonald-Platzman Collective Mode at General Filling Factors: Magneto-Roton Minimum at Half-Filled Landau Level

Abstract

The single mode approximation has proved useful for the excitation spectrum at $\nu =1/3$. We apply it to general fractions and find that it predicts $n$ magneto-roton minima in the dispersion of the Girvin-MacDonald-Platzman collective mode for the fractional quantum Hall states at $\nu =n/(2n+1)$, and one magneto-roton minimum for both the composite Fermi sea and the paired composite fermion state. Experimental relevance of the results will be considered.

5 pages, 6 figures

References in corpus (3)

• Composite Fermions in the Hilbert Space of the Lowest Electronic Landau Level
• Possibility of p-wave pairing of composite fermions at $\nu =1/2$
• Fermi-sea-like correlations in a partially filled Landau level

Cited by in corpus (11)

• Impact of disorder on the 5/2 fractional quantum Hall state
• Positions of the magnetoroton minima in the fractional quantum Hall effect
• Neutral Collective Modes in Spin-Polarized Fractional Quantum Hall States at Filling Factors 1/3, 2/5, 3/7, and 4/9
• Anomalously low magnetoroton energies of the unconventional fractional quantum Hall states of composite fermions
• Splitting of Girvin-MacDonald-Platzman density wave and the nature of chiral gravitons in fractional quantum Hall effect
• Fractional quantum Hall effect at the filling factor $\nu =5/2$
• Roton minimum at $\nu =1/2$ filled fractional quantum Hall effect of Bose particles
• Parametrization and thermodynamic scaling of pair correlation functions for the Fractional Quantum Hall Effect
• Static structure factor and the dispersion of the Girvin-MacDonald-Platzman density mode for fractional quantum Hall fluids on the Haldane sphere
• Splitting of roton minimum in the ν=5/2 Moore-Read state
• Collective excitations in quantum Hall liquid crystals: Single-mode approximation calculations