Landau Level Mixing and Levitation of Extended States in Two Dimensions

Abstract

We study the effects of mixing of different Landau levels on the energies of one-body states, in the presence of a strong uniform magnetic field and a random potential in two dimensions. We use a perturbative approach and develop a systematic expansion in both the strength and smoothness of the random potential. We find the energies of the extended states shift {\em 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.