Behavior of the contacts of Quantum Hall Effect devices at high currents : an electronic thermometer

TL;DR

This study investigates contact resistance behavior in Quantum Hall Effect devices at high currents, revealing its potential as an electronic thermometer for the Hall fluid, with implications for metrological precision.

Contribution

It provides experimental insights into contact resistance dynamics at high currents and proposes using it as a thermometer for the Quantum Hall regime.

Findings

Contact resistance increases with current and width of the Hall bar.

Critical current for contact resistance varies linearly or sublinearly with width.

Heated regions at contacts develop and extend with increasing current.

Abstract

This paper reports on an experimental study of the contact resistance of Hall bars in the Quantum Hall Effect regime while increasing the current through the sample. These measurements involve also the longitudinal resistance and they have been always performed before the breakdown of the Quantum Hall Effect. Our investigations are restricted to the $i=2$ plateau which is used in all metrological measurements of the von Klitzing constant $R_K$. A particular care has been taken concerning the configuration of the measurement. Four configurations were used for each Hall bar by reversing the current and the magnetic field polarities. Several samples with different width have been studied and we observed that the critical current for the contact resistance increases with the width of the Hall bar as previously observed for the critical current of the longitudinal resistance. The critical currents exhibit either a linear or a sublinear increase. All our observations are interpreted in the current understanding of the Quantum hall effect brekdown. Our analysis suggests that a heated region appears at the current contact, develops and then extends in the whole sample while increasing the current. Consequently, we propose to use the contact resistance as an electronic thermometer for the Hall fluid.