Landauer-type formulation of quantum-Hall transport: Critical currents and narrow channels

Landauer-type formulas are derived for two-dimensional quantum-Hall transport in the extreme quantum limit ({}ωc{→}{∞}) for an arbitrary current through an electron system confined to a channel. For narrow channels the problem is mapped into a one-dimensional ordinary (B=0) transport problem. An expression for the critical current and a description of the breakdown of the dissipationless transport are obtained. We find that it is possible to have quantization of the Hall resistance even when the magnetoresistance is nonzero.