Breakdown of the dissipationless quantum Hall state: Quantised steps and analogies with classical and quantum fluid dynamics

The breakdown of the integer quantum Hall effect at high currents sometimes occurs as a series of regular steps in the dissipative voltage drop measur ed along the Hall bar. The steps were first seen clearly in two Hall bars u sed to maintain the US Resistance Standard, but have also been reported in other devices. It is proposed that the origin of the steps can be understoo d in terms of an instability in the dissipationless flow at high election d rift velocities. The instability is induced by impurity- or defect-related inter-Landau level scattering processes in local microscopic regions of the Hall bar. Electron-hole pairs (magneto-excitons) are generated in the quan tum Hall fluid in these regions and that the electronic motion can be envis aged as a quantum analogue of the von Karman vortex street which forms when a classical fluid flows past an obstacle.