THE QUANTUM HALL-EFFECT IN OPEN CONDUCTORS

This chapter discusses transport in a high magnetic field in conductors that confine a two-dimensional electron gas. The chapter also discusses basic elements of electrical conduction, the scattering problem, the current response due to differing chemical potentials. Scattering that the carrier undergoes in the reservoir completely randomizes the energy and phase of the carrier such that a carrier entering the conductor bears no phase and energy relationship to an exiting carrier. Entering and leaving the reservoir is treated as an irreversible event. Using the relations between currents and chemical potentials, one can determine the resistance for a given configuration of current sources and sinks and voltage probes. The chapter discusses two cases explicitly—the case of a two-probe conductor and the case of a resistance measurement in a four-probe setup. The reciprocity of the resistances is the experimentally observed symmetry of electric conduction. The local scattering problem investigated here is a complete solution of reservoir-to-reservoir transmission only under a set of very restrictive conditions: It is a complete solution if every carrier that has been transmitted past the local region of the saddle has a probability of one to leave the constriction in the forward direction, and if every carrier that is reflected leaves the constriction in the backward direction with a probability of one. © 1992, Academic Press Inc.