Electron Localization in a Two-Dimensional System in Strong Magnetic Fields. II. Long-Range Scatterers and Response Functions

A computer simulation is performed to study the problem of the Anderson localization in a two-dimensional electron system in strong magnetic fields. Scatterers with a long-range Gaussian potential are assumed and the localization criterion based on the Thouless number g(L) is employed. The states are shown to be exponentially localized except those in the vicinity of the center of the Landau level. Large statistical fluctuations inherent to the case of long-range scatterers prevent accurate determination of the detailed energy dependence of the inverse localization length. Response functions such as the Hall conductivity, the dynamical conductivity, and the lineshape of the cyclotron resonance are also calculated and compared with the results of the single-site approximation. The peak values of the diagonal conductivity are shown to be larger than the results calculated in the single-site approximation.