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The level broadening and transport properties of a two-dimensional system under extremely strong magnetic fields are investigated in the single-site approximation (SSA). At high concentrations of scatterers, the SSA approaches the simple damping theoretical approximation. At low concentrations, many impurity bands associated with each bound state of an isolated scatterer appear, and the nonexistence of continuous states in this system causes a singular level with zero width in case of scatterers with a δ-potential. The peak value of the conductivity of the impurity band with the angular momentum m is given by \ (2 l^2N₈ (N+m+1/2) e^2/^2\), where N is the Landau quantum number and N i is the concentration of scatterers. The density of states and the conductivity are calculated explicitly for a model system which contains scatterers with the Gaussian potential.
Tsuneya Ando (Sat,) studied this question.