Duality Relation among Periodic Potential Problems in the Lowest Landau Level

K. Ishikawa, N. Maeda, T. Ochiai, H. Suzuki

Published 1997-04-03, updated 1998-06-16Version 2

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.