Quenching of the Hall Effect

We argue that for ballistic transport through a narrow conductor (of width W) a threshold magnetic field exists below which the Hall resistance vanishes. The field is of order (h/e)kF^_^-1W^-3, and is reached when the transverse wavelength of quantum edge states becomes comparable to the width. This is offered as a mechanism for the quenching of the Hall effect discovered experimentally in a narrow two-dimensional electron-gas wire by Roukes et al.