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

Accurate measurements have been made of the quantized Hall resistance (QHR) corresponding to the quantum number i = 2, R_H (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 R_H (2) is independent of the magnetic flux density to within 1 part in 10⁸. The ratio of R_H (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.