Gated-region transport in the quantum Hall effect

We study the quantum Hall effect in samples in which a portion of the longitudinal conduction path is gated. Full magnetic-field sweeps were taken on a sample consisting of a gated Hall bar geometry. These data yielded plateaus in longitudinal resistance, as the gate voltage is varied, for the integer filling factor in the bulk, as previously observed, and plateaus for the case of a fixed integer number of transmitted edge states under the barrier as the gate voltage and the magnetic field are varied. For a significant portion of the Shubnikov de Haas sweeps, the barrier region dominates the characteristic conductance and Fourier analysis allows one to determine the variation of the carrier concentration in the gated region as a function of gate voltage.