Alfred Scharff Goldhaber and M L Horner 2007 J. Phys. A: Math. Theor. 40 14343 doi:10.1088/1751-8113/40/48/002
Single-particle analog to the fractional quantum Hall effect
Alfred Scharff Goldhaber1 and M L Horner2
Show affiliationsWe study the spectrum of states, in a plane perpendicular to a uniform magnetic field, for an electron restricted to the lowest Landau level in the presence of randomly distributed, repulsively correlated electric impurities. The lowest energy band in this spectrum would be the lowest Landau level if there were an effective magnetic flux density downshifted by an integer multiple of the impurity density. The downshift is precisely half that for the corresponding electron density in the composite-fermion picture of the fractional quantum Hall regime. Although the work is numerical, the striking result confirms heuristic arguments based on simple adiabatic calculations. This raises a possibility that further development of adiabatic methods might allow deduction of composite-fermion theory for the fractional quantum Hall effect, starting with spin-up electrons restricted to the lowest Landau level and interacting by Coulomb forces.
- PACS
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71.10.Pm Fermions in reduced dimensions (anyons, composite fermions, Luttinger liquid, etc.)
- MSC
- Subjects
- Dates
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Issue 48 (30 November 2007)
Received 5 September 2007, in final form 18 October 2007
Published 14 November 2007
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Single-particle analog to the fractional quantum Hall effect
Alfred Scharff Goldhaber and M L Horner 2007 J. Phys. A: Math. Theor. 40 14343
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