ABSTRACT
Mesoscopic transport is found experimentally that when we measure a sample of high mobility and small size, the current is always finite, though the transport is ballistic. Since 1985 many mesoscopic experiments have been conducted using miniature Hall bridges fabricated on both metallic and semiconducting samples. With macroscopic conductors, the probes represent a minor perturbation. But for a small conductor the probe can very well be the dominant source of scattering. But this is not the main problem. It is likely that there will be more of lessinvasive microscopic measurements as nanotechnology progresses, for example, using weakly coupled scanning tunneling probes. Mesoscopic measurements are strongly affected by quantum interference effects unless the distance of the probes from the scatterer is much greater than the phase-relaxation length. The chapter concludes that backscattering by the gate potential does not destroy the quantized Hall effect.
