Random magnetic impurities and the Landau problem Original Research Article

The 2-dimensional density of states of an electron is studied for a poissonian random distribution of point vortices carrying α flux in units of the quantum of flux. It is shown that, for any given density of impurities, there is a transition, when α ≅ 0.3–0.4, from an “almost 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.