High Landau levels in a smooth random potential for two-dimensional electrons

We study the density of two-dimensional electronic states for high Landau levels in a perpendicular magnetic field and smooth random potential. The theory developed applies if the correlation radius of a random potential is larger than the magnetic length. Under this condition the exact summation of the diagram series for all the orders of perturbation theory is performed. The density of states represents a system of Gaussian peaks with the width Γ decreasing with energy E as ${\mathit{E}}^{\mathrm{-}1/4}$. The magnetic-field dependence of the width is Γ∝ √B, if the correlation radius is smaller than the classical Larmor radius. In the opposite case Γ does not depend on B. If the correlation radius is smaller than the magnetic length, the self-consistent Born approximation, generalized to the case of smooth potential, applies.