Duality Relation among Periodic Potential Problems in the Lowest Landau Level
Abstract
On the basis of a magnetic von Neumann lattice representation, we study a two-dimensional electron in a uniform magnetic field and obtain one-particle spectra of various periodic potential problems in the lowest Landau level. In a periodic array of short-range potentials, we find a duality relation between a period of the potential and a period of the magnetic von Neumann lattice. This relation is explicitly seen in the structure of the energy spectra, which consist of the Hofstadter-type bands and flat bands. We also show that the periodic potential problem in the lowest Landau level corresponds to a tight-binding model with finite-range hopping terms.Keywords
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