Compendium for precise ac measurements of the quantum Hall resistance

Abstract

Abstract. In view of the progress achieved in the field of the ac quantum Hall effect, the Working Group of the Comité Consultatif d'Électricité et Magnétisme (CCEM) on the AC Quantum Hall Effect asked the authors of this paper to write a compendium which integrates their experiences with ac measurements of the quantum Hall resistance. In addition to the important early work performed at the Bureau International des Poids et Mesures and the National Physical Laboratory, UK, further experience has been gained during a collaboration of the authors' institutes NRC, METAS, and PTB, and excellent agreement between the results of different national metrology institutes has been achieved. This compendium summarizes the present state of the authors' knowledge and reviews the experiences, tests and precautions that the authors have employed to achieve accurate measurements of the ac quantum Hall effect. This work shows how the ac quantum Hall effect can be reliably used as a quantum standard of ac resistance having a relative uncertainty of a few parts in 10 8 .

Quantum resistance standard accuracy close to the zero-dissipation state

“…The understanding of the frequency dependence is beyond the scope of the paper. However, let us just remark that the linear frequency dependent term has a significant amplitude of −3.07 × 10 −7 /kHz in configuration C A that could result from losses in capacitances as was observed at higher frequency (a few kHz) 6 . The extrapolation of (∆R/R) f to f = 0 Hz measured in configurations C A and C B for each current results in ∆R/R CA (I) and ∆R/R CB (I) respectively, the weighted mean value ∆R/R CAB (I) of which can then be calculated.…”

A programmable quantum current standard from the Josephson and the quantum Hall effects

“…Thereby, the unit ohm can be currently maintained in national metrology institutes (NMIs) with a relative uncertainty of 1 × 10 −9 . The application of the QHE in metrology was more recently enlarged by its implementation in the alternating current (AC) regime 9 and by the development of quantized Hall array resistance standards (QHARS) 5,10 . These successes rely on a technique of multiple connection which cancels the effect of any impedance connected in series to the Hall bar terminals 11 .…”

“…The PJAVS maintains the voltage V J between the nodes A and B. The QHR of resistance R H is connected at these nodes using a triple series connection (a similar connection scheme is used in AC regime 9,26 ) with the peculiarity that a CCC winding of number of turns N JK is inserted in each of the three wires connecting the node B to the terminals of the Hall bar. A CCC auxiliary winding of N turns is connected to different external circuits.…”

Digitally assisted coaxial bridge for automatic quantum Hall effect measurements at audio frequencies

“…The investigation of the Quantum Hall Effect (QHE) requires the use of coaxial ac bridges to compare the Quantum Hall Resistance (QHR) to calculable resistance standards at audio frequencies [1], [2], [3]. Such dedicated bridges are optimized to give the highest accuracy in impedance comparison [4].…”