Symmetries of the Resistance of Mesoscopic Samples in the Quantum Hall Regime

TL;DR

This paper explores novel symmetry properties of resistance in mesoscopic quantum Hall samples, revealing new relations between measurements with different contact configurations, depending on the system's quantum Hall transition state.

Contribution

It identifies and characterizes new resistance symmetries in mesoscopic samples in the quantum Hall regime, extending previous findings from macroscopic systems.

Findings

Discovery of new resistance symmetries related to contact configurations.

Symmetries depend on whether the system is above or below a quantum Hall transition.

Related symmetries observed in macroscopic samples previously.

Abstract

The symmetry properties of the resistance of mesoscopic samples in the quantum Hall regime are investigated. In addition to the reciprocity relation, our samples obey new symmetries, that relate resistances measured with different contact configurations. Different kinds of symmetries are identified, depending on whether the magnetic field value is such that the system is above, or below, a quantum Hall transition. Related symmetries have recently been reported for macroscopic samples in the quantum Hall regime by Ponomarenko {\it et al.} (Solid State Commun. {\bf 130}, 705 (2004)), and Karmakar {\it et al.} (Preprint cond-mat/0309694).