On the phonon-assisted breakdown of the dissipationless quantum Hall effect

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Abstract
The collapse of the dissipationless current flow observed in the GaAs-AlxGa1-xAs heterostructures at high currents is explained as due to the spontaneous emission of phonons. The dissipative transfer of electrons along the electric field accompanied by the phonon emission starts when their drift velocity exceeds the speed of sound provided that both initial occupied and final empty states have energies equal to the Fermi energy. With the Fermi energy inside the gap between the Landau sub-bands the transitions involve only the localised and extended states which form the energy spectrum of the inhomogeneous sample in this energy interval.