# Random Magnetic Impurities and the Landau Problem

### Jean Desbois 1, Cyril Furtlehner 1, Stephane Ouvry 1

#### Nuclear Physics B 453 (1995) 759-776

The 2-dimensional density of states of an electron is studied for a Poissonian random distribution of point vortices carrying $\\alpha$ flux in unit of the quantum of flux. It is shown that, for any given density of impurities, there is a transition, when $\\alpha\\simeq 0.3-0.4$, from an älmost free\' density of state -with only a depletion of states at the bottom of the spectrum characterized by a Lifschitz tail- to a Landau density of state with sharp Landau level oscillations. Several evidences and arguments for this transition -numerical and analytical- are presented.

• 1. Division de Physique Théorique, IPN,
Université Paris XI - Paris Sud