Magneto-roton theory of collective excitations in the fractional quantum Hall effect

S. M. Girvin, A. H. MacDonald, and P. M. Platzman
Phys. Rev. B 33, 2481 – Published 15 February 1986
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Abstract

We present a theory of the collective excitation spectrum in the fractional quantum Hall effect which is closely analogous to Feynman’s theory of superfluid helium. The predicted spectrum has a large gap at k=0 and a deep magneto-roton minimum at finite wave vector, in excellent quantitative agreement with recent numerical calculations. We demonstrate that the magneto-roton minimum is a precursor to the gap collapse associated with the Wigner crystal instability occurring near ν=(1/7). In addition to providing a simple physical picture of the collective excitation modes, this theory allows one to compute rather easily and accurately experimentally relevant quantities such as the susceptibility and the ac conductivity.

  • Received 16 September 1985

DOI:https://doi.org/10.1103/PhysRevB.33.2481

©1986 American Physical Society

Authors & Affiliations

S. M. Girvin

  • Surface Science Division, National Bureau of Standards, Gaithersburg, Maryland 20899

A. H. MacDonald

  • National Research Council of Canada, Ottawa, Canada, K1A 0R6

P. M. Platzman

  • AT&T Bell Laboratories, Murray Hill, New Jersey 07974

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Issue

Vol. 33, Iss. 4 — 15 February 1986

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