Theory of contacts in a two-dimensional electron gas at high magnetic fields

General properties of a contact in a two-dimensional electron gas (2D EG), where more than one Landau level is occupied at high magnetic fields, and is quantitatively analyzed on the basis of a Landauer-B\"uttiker formalism. When acting as a current source (drain), a contact generally populates different Landau levels to different degrees. When acting as a voltage probe, a contact does not generally indicate a mean value of the chemical potentials of different Landau levels. A voltage-probe contact works also to partially equalize populations of different Landau levels. These properties, first pointed out qualitatively by B\"uttiker, are quantitatively analyzed in terms of n² parameters when n Landau levels are occupied in the 2D EG. The analysis is applied to the n=2 case to calculate characteristic resistances of multiprobe samples. Results of recent experiments are explained on the basis of the analysis. The properties of electrical transport as well as the properties of energy transmission and dissipation in multiprobe samples are quantitatively discussed.