Current-voltage characteristic in narrow channels and low-voltage breakdown of the quantum Hall effect.

Abstract

Low-voltage breakdown of the quantum Hall effect is considered in narrow quasi-two-dimensional channels subjected to a strong perpendicular magnetic field. The interaction of electrons with acoustical (deformation or piezoelectric) phonons leads to a substantial dissipation at the 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 large. Nonheating negative differential conduction, ${\mathit{dj}}_{\mathit{x}}$/${\mathit{dE}}_{\mathit{x}}$0, when an electric field ${\mathit{E}}_{\mathit{x}}$ is applied along the channel, is possible for drift velocities ${\mathit{v}}_{\mathit{D}}$ smaller (${\mathit{v}}_{\mathit{D}}$s) or much smaller (${\mathit{v}}_{\mathit{D}}$\ensuremath{\ll}s) than the speed of sound s as well for ${\mathit{v}}_{\mathit{D}}$>s. The current-voltage characteristic (CVC) ${\mathit{j}}_{\mathit{x}}$=${\mathit{j}}_{\mathit{x}}$(${\mathit{E}}_{\mathit{x}}$), evaluated numerically for a number of qualitatively different cases, is substantially nonlinear if ${\mathit{v}}_{\mathit{D}}$ is not too small. The results are in good agreement with the experimental results by von Klitzing et al. for low breakdown velocities (${\mathit{v}}_{\mathit{D}}$\ensuremath{\sim}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 al. is explained as well. The anisotropy of the electron-phonon interaction in MOS structures and its substantial influence on the CVC and breakdown velocities is also considered. The dissipation depends very strongly on the frequency \ensuremath{\Omega} of the confining potential if ${\mathit{v}}_{\mathit{D}}$ is not too large. In contrast with Martin and Feng [Phys. Rev. Lett. 64, 1971 (1990)], for sufficiently small \ensuremath{\Omega}, an exponential suppression of the dissipation occurs due to intralevel-intraedge acoustic-phonon-assisted transitions.