Quantized Hall Effect in the Presence of Backscattering

The quantized Hall effect comprises edge states flowing in opposite directions on opposite edges of a two-dimensional electron gas. In a narrow wire, the presence of a potential barrier in the wire can cause the state to be reflected back into the oppositely directed state at the outer edge of the sample. Experiments on narrow (\ensuremath{\sim}1 \ensuremath{\mu}m) $\mathrm{GaAs}\ensuremath{-}{\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ wires with short cross gates confirm that backscattering is caused by the barrier drawn up by the gate. The barrier, by reflecting some fraction of the states, causes quantized plateaus in any four-probe measurement of resistance.