Nonclassical scattering dynamics in the quantum Hall regime.

Abstract

We consider a large class of two-dimensional systems of electrons in a static disorder potential and subject to an in-plane electric field and to a strong perpendicular magnetic field. The time evolution of the single-particle states is investigated and found to be crucial for quantum Hall behavior. The macroscopic Hall current is carried by the nonadiabatic states. Quantum Hall behavior results when the Fermi energy lies in a range of adiabatic levels. Linear-response theory is inadequate to describe the quantum-mechanical single-particle scattering process in the quantum Hall regime. The general results are illustrated by an explicit weak-disorder model, where the scattering process and the nature of dc-insulating and -conducting states can be understood in detail. We stress analogies with one-dimensional conductance in the presence of disorder.