Dynamics of nonequilibrium electrons at the breakdown of the quantum Hall effect

Abstract

We have analysed the energy excitation and relaxation of hot electrons close to the breakdown of the quantum Hall effect. Hot electrons were generated by a periodic set of constrictions (parallel microscopic trenches or antidot arrays). For the relaxation experiments, hot electrons are injected into two-dimensional electron systems (2DES) of various mobilities, with Hall fields below the breakdown value. The resistivity of the 2DES is measured as a function of the distance from the injection front. The characteristic decay length of the resistivity was found to strongly increase with current in a rather narrow range of currents until the dissipation persists over the entire sample at the breakdown. The results are compared with calculations on the basis of a nonequilibrium between the excitation and relaxation of hot electrons. Energy relaxation lengths from 0.3 to 3 μm were deduced, which are comparable to the mean free path. Thus, the inelastic scattering, which is responsible for the breakdown of the QHE, is strongly related to elastic Coulomb scattering. Spatially resolved measurements of the electron heating were performed in samples with antidot and wire arrays, and with macroscopic constrictions. An avalanche-like heating of electrons could be observed in the antidot array, but the data have not yet been reconciled with a quantitative picture.