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

Low-voltage breakdown of the quantum Hall effect is considered in narr ow quasi-two-dimensional channels subjected to a strong perpendicular magnetic field. The interaction of electrons with acoustical (deformat ion or piezoelectric) phonons leads to a substantial dissipation at th e edges of the channel, due to electron transitions between the edges states. It is the main dissipation if the channel width W is not too l arge. Nonheating negative differential conduction, dj(x)/dE(x) < 0, wh en an electric field E(x) is applied along the channel, is possible fo r drift velocities upsilon D smaller (upsilon(D) < s) or much smaller (upsilon(D) << s) than the speed of sound s as well for upsilon(D) > s . The current-voltage characteristic (CVC) j(x) = j(x)(E(x)), evaluate d numerically for a number of qualitatively different cases, is substa ntially nonlinear if upsilon(D) is not too small. The results are in g ood agreement with the experimental results by von Klitzing et al, for low breakdown velocities (upsilon(D) similar to s/20) in metal-oxide- semiconductor (MOS) structures. An increase by orders of magnitude in the dissipation, before breakdown, as observed, e.g., by Komiyama et a l, is explained as well. The anisotropy of the electron-phonon interac tion in MOS structures and its substantial influence on the CVC and br eakdown velocities is also considered. The dissipation depends very st rongly on the frequency Omega of the confining potential if upsilon(D) is not too large. In contrast with Martin and Feng [Phys. Rev. Lett. 64, 1971 (1990)], for sufficiently small Omega, an exponential suppres sion of the dissipation occurs due to intralevel-intraedge acoustic-ph onon-assisted transitions.