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Landau level mixing and the fractional quantum Hall effect

I. Sodemann and A. H. MacDonald
Phys. Rev. B 87, 245425 – Published 21 June 2013

Abstract

We derive effective Hamiltonians for the fractional quantum Hall effect in n=0 and n=1 Landau levels that account perturbatively for Landau-level mixing by electron-electron interactions. To second order in the ratio of electron-electron interaction to cyclotron energy, Landau-level mixing is accounted for by constructing effective interaction Hamiltonians that include two-body and three-body contributions characterized by Haldane pseudopotentials. Our study builds upon previous treatments, using as a stepping stone the observation that the effective Hamiltonian is fully determined by the few-body problem with N=2 and N=3 electrons in the partially filled Landau level. For the n=0 case we use a first quantization approach to provide a compact and transparent derivation of the effective Hamiltonian which captures a class of virtual processes omitted in earlier derivations of Landau-level-mixing corrected Haldane pseudopotentials.

  • Figure
  • Received 10 April 2013

DOI:https://doi.org/10.1103/PhysRevB.87.245425

©2013 American Physical Society

Authors & Affiliations

I. Sodemann and A. H. MacDonald

  • Department of Physics, University of Texas at Austin, Austin, Texas 78712, USA

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Issue

Vol. 87, Iss. 24 — 15 June 2013

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