Symmetries of the resistance of mesoscopic samples in the quantum Hall regime

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 et al. Solid State Commun. 130 705 (2004), and Karmakar et al. (preprint cond-mat∕0309694).