Duality Relation among Periodic Potential Problems in the Lowest Landau Level

Abstract

Using a momentum representation of a magnetic von Neumann lattice, we study a two-dimensional electron in a uniform magnetic field and obtain one-particle spectra of various periodic short-range potential problems in the lowest Landau level.We find that the energy spectra satisfy a duality relation between a period of the potential and a magnetic length. The energy spectra consist of the Hofstadter-type bands and flat bands. We also study the connection between a periodic short-range potential problem and a tight-binding model.

6 pages, 3 figures, final version to appear in PRB

References in corpus (2)

• Magnetic von-Neumann lattice for two-dimensional electrons in the magnetic field
• Flux State in von Neumann lattice and Fractional Hall Effect

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