Journal
PHYSICAL REVIEW B
Volume 87, Issue 24, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.87.245425
Keywords
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Funding
- Welch Foundation [TBF1473]
- DOE Division of Materials Sciences and Engineering [DE-FG03-02ER45958]
- NRI SWAN program
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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.
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