Transmission probabilities and the quantum Hall effect

A scattering approach to magneto-transport permits the discussion of open conductors with current and voltage terminals. This approach leads to generalized longitudinal and generalized Hall resistances which are determined by the current carrying states at the Fermi energy. In samples small compared to the distance over which current carrying states equilibrate, the contact properties are crucial in determining whether the Hall voltage is quantized or not. Simple situations in which both the longitudinal and the Hall resistance are simultaneously quantized at values unrelated to the bulk properties of the sample are emphasized. The departure from the quantum Hall plateaus in narrow conductors is discussed in terms of intrinsic Breit-Wigner resonances. © 1990.