Heating of two-dimensional electrons by a high electric field in a quantizing magnetic field: Consequences in Landau emission and in the quantum Hall effect.

Abstract

We study the electric-field-induced heating process of a two-dimensional electron gas in the quantum-Hall-effect (QHE) regime. We present both theoretical and experimental results. We calculate the inter-Landau-level transition probabilities under high electric field, in the presence of both phonon and impurity scattering. We deduce from the theoretical investigations the total emitted power of the cyclotron emission as a function of the electric-field intensity. We perform both cyclotron emission and quantum transport experiments, on ${\mathrm{Ga}}_{\mathit{x}}$${\mathrm{Al}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As/GaAs and ${\mathrm{Ga}}_{\mathit{x}}$${\mathrm{In}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As/GaAs heterojunctions, at liquid-helium temperature and magnetic fields up to 8 T, using samples with different geometry. We therefore distinguish several cyclotron emission regimes and we demonstrate, with theoretical arguments, that the average electric field in the sample is not a good physical parameter in the description of the heating process and of the cyclotron emission for a two-dimensional electron gas. We finally present experimental results which tend to prove that the local electric field can be high enough in some parts of the sample, to induce inter-Landau-level scattering, and consequently to generate the cyclotron emission and to induce the breakdown of the quantum Hall effect. The role of the microscopic local electric field is confirmed by the observation of the emitted power amplification in the plateaus regime of the QHE. This phenomenon is due to the modification of the current path geometry and the enhancement of the local electric field in the vicinity of the contact point in the QHE regime.