Conduction in a strong field in two dimensions: The quantum Hall effect

Abstract

Several conditions under which a magnetic field can be considered to be strong in comparison with a random scattering potential are distinguished. These are the maximum magnitude of the scattering potential small compared with Landau-level separation, large spatial separation of otherwise arbitrary scattering centers compared with the quantum size of Landau states, and smoothness of the scattering potential on this scale. In all three cases, by somewhat different mechanisms, extended states exist and the ideal quantum Hall resistance is found. The case of scattering centers separated by a smoothly varying potential can also be solved. The actual experimental conditions are likely to involve aspects of all three conditions.