Vanishing hall voltage in a quasi-one-dimensional $\mathrm{Ga}\mathrm{A}\mathrm{s}-{\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ heterojunction

We have measured the Hall voltage developed across a narrow, high-mobility two-dimensional electron gas of variable width. For narrow channels, the Hall voltage vanishes when the prependicular magnetic field is reduced below a certain, critical value. If the magnetic field is kept constant as the width of the channel is reduced, the Hall voltage shows large departures from the classically expected result.