Voltage-controlled dissipation in the quantum Hall effect in a laterally constricted two-dimensional electron gas

We have observed controlled, low-voltage breakdown of the quantum Hall effect in GaAs-${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As heterostructures with lateral constrictions a few micrometers in width. The breakdown characteristics show structure at voltages corresponding to the cyclotron energy for even filling factors or the exchange-enhanced Zeeman energy for odd filling factors. Analysis of these results in terms of a simple model implies that the dissipation process involves interlevel as well as intralevel scattering, and therefore that large potential gradients must be present in the two-dimensional electron gas. We interpret structure at multiples of the cyclotron energy for even filling factors in terms of a multiple-current-path model.