Electron Localization in a Two-Dimensional System in Strong Magnetic Fields. I. Case of Short-Range Scatterers

A computer simulation is performed to study localization of a two-dimensional electron system in strong magnetic fields. Scatterers with short-range δ-potentials are assumed, and the localization criterion based on the Thouless number g(L) is employed. It is shown that states are localized exponentially except in the vicinity of the center of each Landau level. The decay rate of the localized wave function, i.e., the inverse localization length, approaches zero smoothly at the center. This suggests that only the states just at the center of the Landau level are not localized and all the other states are exponentially localized, although the localization length is extremely large near the center. The energy range where the localization length is extremely large becomes wider with the Landau level index.