Spatial evolution of the generation and relaxation of excited carriers near the breakdown of the quantum Hall effect

Abstract

We have measured the generation and relaxation of excited carriers along their drift direction near the breakdown of the quantum Hall effect (QHE). The dissipative resistivity ρ xx ( x) at current densities close to the critical value for the QHE breakdown was measured as a function of the distance x from the electron injection at x=0. By injecting “cold” electrons into constrictions at supercritical current levels, the evolution of the breakdown along the drift direction was monitored. After a smooth increase of the resistivity with the drifting distance, an avalanche-like rise towards a saturation value occurs. Drastic changes of the resistivity profiles with the applied current were found in a narrow range around the critical current. The observed behavior is attributed to impurity-assisted tunneling between Landau levels. By injecting hot electrons (excited in a periodic set of constrictions) into a region with subcritical current density, the relaxation process was analyzed. Inelastic relaxation lengths with typical values in the range from 0.3 to 4 μm were found, which agree within 10% with the elastic mean free path determined from the Hall mobility at zero magnetic field. We conclude that the energy relaxation process is triggered by scattering at impurity potentials.