Resistance metrology based on the quantum Hall effect

The Quantum Hall effect (QHE), a macroscopic effect of solid state physics, provides a universal representation of the unit of resistance which depends on the elementary charge e and the Planck constant h only. If implemented according to specific technical guidelines, the quantum resistance standard can be reproduced with a relative uncertainty below one part in 109. Calibrations of wire resistors in terms of the QHE can be carried out with similarly low uncertainties by using resistance bridges equipped with cryogenic current comparators, the performance of which relies on the magnetic flux sensitivity of superconducting quantum interference devices (SQUID). Using a special connection technique, the fundamental properties of the QHE allow the fabrication of arrays combining a large number of single Hall bars connected in series or in parallel and which demonstrate quantum accuracy. Similar to the case of voltage metrology with Josephson array voltage standards, an improvement of resistance metrology is expected from the availability of quantum Hall array resistance standards (QHARS). The QHE Wheatstone bridge, which is another application of the same connection technique, opens the way to new universality tests of the QHE with a relative uncertainty below one part in 1011. At frequencies in the kilohertz range, the recent progress in the application of coaxial bridges to the QHE allows metrologists to operate a quantum resistance standard with alternating current reaching an accuracy of some parts in 108. Finally, the discovery of the QHE in graphene opens new horizons for the resistance metrology.