How does a strong magnetic field destroy localization in two-dimensional disordered systems?

Abstract

Two dimensional disorder in a strong magnetic field is investigated in terms of random matrix theory and in comparison to the conventional Anderson tight-binding model. Disorder is introduced by an ensemble average over a random potential which has to be projected onto single Landau bands. This leads to a random matrix problem for single Landau levels whose special properties are examined. We describe a method which allows a proper projection of various random potentials, specified by a correlation function, onto arbitrary subspaces. The matrix elements of the Hamiltonian for single Landau bands are strongly correlated along the diagonals. The influence of such correlations on the localization properties is examined for a disk geometry. We obtain a qualitative understanding for the question raised in the title of the paper.