- 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.