Low-voltage breakdown of the quantum Hall effect in narrow channels

Low-voltage breakdown is considered in a quasi-two-dimensional electron gas confined laterally in a narrow channel of width W and subject to a strong perpendicular magnetic field. It is shown that electron-phonon interaction leads to a substantial dissipation due to electron transitions at the edges of the channel and constitutes the main dissipation in the channel if W is not too large. Negative differential conduction is possible when a threshold drift velocity vD is reached. This leads to an instability of the almost dissipationless regime, i.e., to the breakdown of the quantum Hall effect. Under certain conditions the instability is possible for vDs or vD{}s (low-voltage breakdown), where s is the speed of sound. The finite thickness of the channel leads, in general, to breakdown velocities smaller than those pertaining to zero thickness. Good agreement is obtained between the theory and the experimental results of Makerov et al. $fat (---Pis'ma Zh. Eksp. Teor. Phys. 47, 59 (1988) [JETP Lett. 47, 71 (1988)).