Explanation of quantized-Hall-resistance plateaus in heterojunction inversion layers

Abstract

A self-consistent calculation of $\frac{n}{B}$ (inversion layer carrier density divided by magnetic field strength) vs $\frac{1}{B}$ exhibits quantized values over finite ranges of $B$ (plateaus), just as seen in the Hall-resistance measurements of Tsui and Gossard. Electrons here in the inversion layer come from the ionized donors which, because of band bending, have a continuous energy density of states. These states fill or empty as the energy of Landau levels sweeps past them, producing the plateaus.