Disorder and localization in the lowest Landau level in the presence of dilute point scatterers
Date
1999
Authors
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Source Title
Solid State Communications
Print ISSN
0038-1098
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Publisher
Pergamon Press
Volume
112
Issue
3
Pages
157 - 160
Language
English
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Abstract
We study the localization properties of a two-dimensional noninteracting electron gas in the presence of randomly distributed short-range scatterers in very high magnetic fields. We evaluate the participation number of the eigenstates obtained by exact diagonalization technique. At low impurity concentrations we obtain self-averaged values showing that all states, except those exactly at the Landau level, are localized with finite localization length. We conclude that in this dilute regime the localization length does not diverge. We also find that the maximum localization length increases exponentially with impurity concentration. Our calculations suggest that scaling behavior may be absent even for higher concentrations of scatterers.