Heating process in the pre-breakdown regime of the quantum Hall effect: a size-dependent effect

Abstract Our study presents experimental measurements of the contact and longitudinal voltage drops in Hall bars, as a function of the current amplitude. We are interested in the heating phenomenon which takes place before the breakdown of the quantum Hall effect, i.e. the pre-breakdown regime. Two types of samples has been investigated, at low temperature (4.2 and 1.5 K ) and high magnetic field (up to 13 T ). The Hall bars have several different widths, and our observations clearly demonstrate that the size of the sample influences the heating phenomenon. By measuring the critical currents of both contact and longitudinal voltages, as a function of the filling factor (around i=2), we highlight the presence of a high electric field domain near the source contact, which is observable only in samples whose width is smaller than 400 μm .