02-232 J. Bruening, S. Yu. Dobrokhotov, V. A. Geyler, and K. V. Pankrashkin

The geometric structure of the Landau bands (457K, RevTeX 4 with 3 figures) May 21, 02

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Abstract. We have proposed a semiclassical explanation of the geometric structure of the spectrum for the two-dimensional Landau Hamiltonian with a two-periodic electric field without any additional assumptions on the potential. Applying an iterative averaging procedure we approximately, with any degree of accuracy, separate variables and describe a given Landau band as the spectrum of a Harper-like operator. The quantized Reeb graph for such an operator is used to obtain the following structure of the Landau band: localized states on the band wings and extended states near the middle of the band. Our approach also shows that different Landau bands have different geometric structure.

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