Current carrying states in the lowest Landau level

Abstract

We have performed numerical calculations for noninteracting electrons in two dimensions in the high-magnetic-field (lowest-Landau-level) limit in the presence of a random potential. By identifying the first Chern character of each eigenstate, we show directly from the data for sizes varying from scrN=8 flux quanta to scrN=128 that the lowest Landau level has extended eigenstates only at a single energy ${\mathit{E}}_{\mathit{c}}$ (the center of the band). The localization length ξ is found to diverage as (E-${\mathit{E}}_{\mathit{c}}$ ${)}^{\mathrm{-}\nu }$, with ν=2.4±0.1, in agreement with previous calculations.