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)

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.