The control electrons at the level of the elementary charge e was demonstrated experimentally already in the 1980s. Ever since, the production of an electrical current ef, or its integer multiple, at a drive frequency f has been in a focus of research for metrological purposes.This review discusses the generic physical phenomena and technical constraints that influence single-electron charge transport and presents a broad variety of proposed realizations. Some of them have already proven experimentally to nearly fulfill the demanding needs, in terms of transfer errors and transfer rate, of quantum metrology of electrical quantities, whereas some others are currently ‘‘just’’ wild ideas, still often potentially competitive if technical constraints can be lifted. The important issues of readout of singleelectron events and potential error correction schemes based on them are also discussed. Finally, an account is given of the status of single-electron current sources in the bigger framework of electric quantum standards and of the future international SI system of units, and applications and uses of single-electron devices outside the metrological context are briefly discussed.

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Single-electron current sources: Toward a refined definition of the ampere

The quantum Hall effect (QHE) provides an invariant reference for resistance linked to natural constants It is used worldwide to maintain and compare the unit of resistance The reproducibility reached today is almost two orders of magnitude better than the uncertainty of the determination of the ohm in the international system of units SI In this article, mainly the aspects of the QHE relevant for its metrological application are reviewed After a short introduction of the theoretical models describing the integer QHE, the properties of the devices used in metrology and the measurement techniques are described A detailed summary is given on the measurements carried out to demonstrate the universality of the quantized Hall resistance and to assess all the effects leading to deviations of the Hall resistance from the quantized value In addition, the present and future role of the QHE in the SI and the field of natural constants is discussed

https://iopscience.iop.org/article/10.1088/0034-4885/64/12/201/pdf

The quantum Hall effect as an electrical resistance standard

This paper describes the main tests and precautions necessary for both reproducible and accurate results in the use of the quantum Hall effect as a means to establish a reference standard of dc resistance having a relative uncertainty of a few parts in 109.

https://iopscience.iop.org/article/10.1088/0026-1394/40/5/302/pdf

Revised technical guidelines for reliable dc measurements of the quantized Hall resistance

The authors have between them more than 60 years of experience in making electrical measurements in National Measurement Laboratories. These laboratories are the source of measurement standards and techniques for science and engineering and are dedicated to maintaining the international system of units (SI) by establishing and disseminating the values of measurement standards with the lowest possible uncertainty. Careful attention to detail is required in designing measurement systems that eliminate electrical interference and are as simple and as close to first principles as possible. This book draws on their experience by offering guidance and best practice for designing sensitive electrical measurement circuits. In particular the book describes examples that demonstrate the elegance, flexibility and utility of balanced-current coaxial networks in obtaining the ultimate in noise-matching and interference elimination for precise and accurate voltage, current and power measurements. It also updates an earlier book on coaxial AC bridges by including recent AC measurements of quantum Hall resistance to establish a primary quantum standard of impedance and by extending impedance measurements in general to higher frequencies.

Coaxial Electrical Circuits for Interference-Free Measurements

Accurate measurements have been made of the quantized Hall resistance (QHR) corresponding to the quantum number i = 2, RH (2), of two GaAs-based heterostructures using alternating current in the frequency range from 1 Hz to 1,6 kHz. The QHR is compared with a conventional ac reference resistance standard (Vishay type) of the same nominal value. The measurements are made with an alternating current comparator bridge at 1 Hz and with a coaxial ac bridge from 400 Hz to 1,6 kHz. The quantum Hall effect (QHE) sample is connected to the coaxial bridge using a double series connection. An analysis of the circuit properties of the sample shows that this technique of connection is sufficient to define the QHR as a four terminal-pair impedance. It also avoids perturbing effects from small capacitances between the terminals of the sample and from inductive reactances in series with the terminals. At frequencies up to at least 1,6 kHz a central region on the Hall resistance plateau has been observed for which the Hall resistance RH (2) is independent of the magnetic flux density to within 1 part in 108. The ratio of RH (2) to the reference resistance varies by less than 2 parts in 107 from 1 Hz to 1,6 kHz. A significant part of this variation is probably due to the frequency dependence of the reference resistance itself.

https://iopscience.iop.org/article/10.1088/0026-1394/31/5/004/pdf

Accurate AC Measurements of the Quantized Hall Resistance from 1 Hz to 1,6 kHz

The circuit properties of networks which include multiterminal quantum Hall‐effect (QHE) devices are discussed. It is shown that QHE devices can be placed in a series or in parallel using multiple links to give equivalent four‐terminal quantized resistances which are in practice, to a high degree of accuracy, independent of contact resistances to the two‐dimensional electron gas in the samples and of series resistances in the links. The same technique of multiple links can also be used to incorporate QHE devices in resistance or impedance bridges, resulting in a balance condition which is practically unaffected by contact or series resistances. These properties are established using calculations based on equivalent circuits of QHE devices. Metrological applications include the obtainment of accurate reference standards of resistance with values which are multiples or submultiples of individual quantized Hall resistances (QHRs) and, using a resistance bridge, the precise comparison of QHRs. An experimental verification is reported, demonstrating that the effective equivalent resistance of two QHE devices connected in parallel does not differ from nominal by more than a few parts in 109.

François Delahaye

Papers

Series and parallel connection of multiterminal quantum Hall‐effect devices