Quantum Hall Effect: Current Distribution and Existence of Extended States

Abstract

We present a consistent description of the current distribution in the quantum Hall effect, based on two main ingredients: the location of the extended states and the distribution of the electric field. We show that the interaction between electrons produces a boundary line below the Fermi energy, which extends from source to drain. The existence of this line and that of a physical boundary are responsible for the formation of a {\em band} of extended states that carry the Hall current. The number and density of these extended states are determined by the difference between the energy of this equipotential boundary line and the energy of the single extended state that would exist in an infinite system. This is used to prove that the band of extended states is distributed through the bulk of the sample. We explore the distribution of the Hall currents and electric fields in by presenting a model that captures the main features of the charge relaxation processes. Theoretical predictions based on this model and on the preceding theory are used to unambiguously explain recent experimental findings.