Girvin-MacDonald-Platzman collective mode at general filling factors: magneto-roton minimum at half-filled Landau level

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. (C) 2000 Elsevier Science Ltd. All rights reserved.