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The geometric structure of the Landau bands

J. Bruening·S. Yu. Dobrokhotov·V. A. Geyler·K. V. Pankrashkin
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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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J. Bruening, S. Yu. Dobrokhotov, V. A. Geyler, K. V. Pankrashkin. 2002-05-21. The geometric structure of the Landau bands. https://arxiv.org/abs/cond-mat/0205443

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