Broadening of the lowest Landau level by a Gaussian random potential with an arbitrary correlation length: an efficient continued-fraction approach

Abstract

For an electron in the Euclidean plane subjected to a perpendicular constant magnetic field and a homogeneous Gaussian random potential with a Gaussian covariance function we approximate the averaged density of states restricted to the lowest Landau level. To this end, we extrapolate the first nine coefficients of the underlying continued fraction consistently with the coefficients’ high-order asymptotics. The latter derives from the known asymptotic decay of the density of states in the tails. We thus achieve on the one hand a reliable extension of Wegner’s exact result [Z. Phys. B 51, 279 (1983)] for the delta-correlated case to the physically more relevant case of a non-zero correlation length. On the other hand, we have thereby found a paragon for the power of continued-fraction expansions for designing approximations to spectral densities.