Reservoir hypothesis for the quantum hall effect

It is assumed that in modulation‐doped heterojunctions the 2D electron gas is in thermodynamical equilibrium with an external reservoir. In a quantizing magnetic field energy gaps appear in the density of states of the 2D system. This produces, when the magnetic field B increases, oscillations of the density of the free 2D electrons, because of the transfer of electrons into (and out of) the reservoir. It is shown that these oscillations of N 8 induce the formation of plateaus of the Hall resistivity ϱ xy with the exact quantization in h/ie 2 and vanishing values of the resistivity ϱ xx , when the Fermi energy is between Landau levels. The model developed in the triangular well approximation accounts well for the width and shape of the Hall steps and for the ϱ xx behaviour in a magnetic field, in a large range of temperatures.