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Collective excitations in the Ginzburg-Landau theory of the fractional quantum Hall effect

Mar 4, 1991
Published in:
  • Phys.Rev.Lett. 66 (1991) 9, 1220
  • Published: Mar 4, 1991
DOI:
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Abstract: (APS)
The collective excitations of the fractional-quantum-Hall liquid are studied within the Ginzburg-Landau theory. We show that (1) Gaussian fluctuations of the phase of the order parameter correspond to the cyclotron mode with an energy gap of \ensuremath{\Elzxh}{\mathrm{\ensuremath{\omega}}}_{\mathit{c}} at q=0 and a contribution to the static structure factor proportional to \ensuremath{\Vert}q{\mathrm{\ensuremath{\Vert}}}^{2} as q\ensuremath{\rightarrow}0, in accordance with Kohn's theorem, and (2) vortex-antivortex fluctuations give rise to the lowest-Landau-level collective mode with an energy gap that depends only on the Coulomb energy and a static structure factor that vanishes as \ensuremath{\Vert}q{\mathrm{\ensuremath{\Vert}}}^{4} as q\ensuremath{\rightarrow}0.
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