LOW-VOLTAGE BREAKDOWN OF THE QUANTUM HALL-EFFECT IN NARROW CHANNELS

Low-voltage breakdown is considered in a quasi-two-dimensional electro n gas confined laterally in a narrow channel of width W and subject to a strong perpendicular magnetic field. It is shown that electron-phon on interaction leads to a substantial dissipation due to electron tran sitions at the edges of the channel and constitutes the main dissipati on in the channel if W is not too large. Negative differential conduct ion is possible when a threshold drift velocity v(D) 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 th e instability is possible for v(D) < s or v(D) much less than 8 (low-v oltage breakdown), where 8 is the speed of sound. The finite thickness of the channel leads, in general, to breakdown velocities smaller tha n those pertaining to zero thickness. Good agreement is obtained betwe en the theory and the experimental results of Makerov et al.