Quantum Hall Effect and Ohm Metrology

Abstract

The quantum Hall effect (QHE) discovery has revolutionized the ohm metrology: the representation of the unit of resistance is now universal and the ohm can be maintained in each national metrology institute with a relative uncertainty of one part in 10 9 . This breakthrough also results from the development of resistance comparison bridges using cryogenic current comparator (CCC). The fundamental properties of the QHE allow the realization of Quantum Hall Array Resistance Standards (QHARS) by combining a large number of single Hall bars connected in series and/or in parallel. These standards can be as accurate as a single Hall bar. More generally, the multiple connection technique allows metrologists to design useful circuits based on quantum Hall resistors like voltage dividers or Wheatstone bridges. The QHE Wheatstone bridge is particularly suitable for comparing quantum standards. By detecting the unbalance current of this bridge with a CCC, new universality tests of the QHE with a target uncertainty less than 10 11 can be realized.

Inertial-Hall effect: the influence of rotation on the Hall conductivity

“…The IQHE is a macroscopic effect of solid state physics and it is characterized by a quantized Hall conductivity which is given by integer multiples of e 2 /h, where e is the electrical charge and h is the Planck's constant. The quantization of the Hall conductivity has been measured to 1 part in 10 9 [2,3]. This precision reveals the topological nature of the Hall conductivity, which does not depend on the material, geometry and microscopic details of the sample, and makes the IQHE very useful in the field of metrology.…”

Matrix method analysis of quantum Hall effect device connections

“…The accurate measurement of R H has to reject any stray resistance (in dc) or impedance (in ac) which is added by the device contacts and the external wiring. Even though a simple four-terminal connection can be sufficient for dc measurements on a single device, the series or parallel connection of several devices [2,3], the realization of single-chip quantum Hall arrays [4] and measurements in the ac regime [5] ask for more complex connection schemes, usually based on the double-or triple-series connections introduced by Delahaye [2].…”

Application of the quantum Hall effect to resistance metrology

“…The QHE, as well as the Josephson effect [4][5][6] which provides a quantum representation of the volt based on the phenomenological constant K J , the Josephson constant theoretically equal to 2e/h, have revolutionized the representation of electrical units. The possibility to directly link the ampere to the electron charge e by means of electron pumps, based on the Coulomb blockade [7,8], another major quantum effect in condensed matter, is even extensively investigated.…”

“…The electrodes are prolonged at both ends with cylindrical parts of same diameter (part (4)) but larger cylindricity defects. The usable length of the capacitor is then increased from 200 to 400 mm, thereby allowing capacitance variations between 0.3 pF and about 1 pF depending on the displacement length of the moving guard electrode (part (5)). An accurate measurement of this length is carried out with a Michelson interferometer not shown in Fig.…”