Lifshitz-like argument for low-lying states in a strong magnetic field
Institute of Physics, University of Oslo, PO Box 1048 Blindern, 0316 Oslo, Norway
Published online: 15 November 2000
Localization of an electron moving in two dimensions, submitted to a strong magnetic field and scattered by randomly distributed zero-range impurities is investigated. Considering the explicit expression for the density of states obtained by Brézin, Gross and Itzykson, the Lifshitz argument is adapted in order to analyze the unusual power-law behavior of the low energy spectrum. When the impurity density is smaller than the Landau degeneracy, typical configurations of disorder responsible for low energy states are identified as cluster of impurities of well defined form. This allows for an interpretation of low-lying states, localized around these clusters, whose size diverges logarithmically as the energy goes to zero.
PACS: 73.40.Hm – Quantum Hall effect (integer and fractional) / 72.15.Rn – Localization effects (Anderson or weak localization) / 05.30.-d – Quantum statistical mechanics
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2000