Disorder and localization in the lowest Landau level in the presence of dilute point scatterers

We study the localization properties of a two-dimensional noninteracting el ectron gas in the presence of randomly distributed short-range scatterers i n very high magnetic fields. We evaluate the participation number of the ei genstates obtained by exact diagonalization technique. At low impurity conc entrations we obtain self-averaged values showing that all states, except t hose exactly at the Landau level, are localized with finite localization le ngth. We conclude that in this dilute regime the localization length does n ot diverge. We also find that the maximum localization length increases exp onentially with impurity concentration. Our calculations suggest that scali ng behavior may be absent even for higher concentrations of scatterers. (C) 1999 Elsevier Science Ltd. All rights reserved.