Duality relation among periodic-potential problems in the lowest Landau level

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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.