LANDAU-LEVEL MIXING AND LEVITATION OF EXTENDED STATES IN 2 DIMENSIONS

We study the effects of mixing of different Landau-levels on the energ ies of one-body states, in the presence of a strong uniform magnetic f ield and a random potential in two dimensions. We use a perturbative a pproach and develop a systematic expansion in both the strength and sm oothness of the random potential. We find the energies of the extended states shift upward and the amount of levitation is proportional to ( n + 1/2)/B-3 for strong magnetic field, where B is the magnetic field strength and n is the Landau level index.