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We tested a simple digital impedance bridge using two nominally equal resistors to form a 1:1 ratio. We focused on resolution and stability of the detectors. Fluctuations of the source voltages were largely removed through postprocessing of the digitized data, and the measurement results were limited by the detector noise. This detector-limited operating condition was first demonstrated using three modified Keysight 3458A multimeters for measurements of the voltage ratios, achieving 0.01 μV/V type A uncertainty in less than 15 min at 1 kHz. In an effort to extend the applicable frequency range and develop a system with off-the-shelf components, we tested a system using three lock-in detectors for measuring small deviations from the perfect AC ratio of unity magnitude, achieving stabilities and resolutions of 0.1 μV/V in a few hours for each point from 1 kHz to 5 kHz.

We tested a digital impedance bridge in a hybrid structure for comparison of a capacitor with a resistor where the impedance ratio was measured in two separate parts. The modulus of the impedance ratio was matched arbitrarily close to the input-to-output ratio, in magnitude, of a two-stage inductive voltage divider by adjusting the operating frequency of the bridge; the residual deviation between the two together with the phase factor of the impedance ratio was measured using a custom detection system based on a four-channel 24-bit digitizer. The ratio of the inductive voltage divider was calibrated, in situ , using a conventional four-arm bridge with two known capacitors. Fluctuations of the source voltages were largely removed through postprocessing of the digitized data, and the measurement results were limited by the digitizer error. We have achieved an overall bridge resolution and stability of 0.02 μF/F in 2 h for measuring a 100-pF capacitor relative to a 12 906-Ω resistor at 1233 Hz. The relative combined standard uncertainty ( k = 1) is 0.13 μF/F, dominated by the digitizer error.

Monolayer epitaxial graphene (EG) has been shown to have clearly superior properties for the development of quantized Hall resistance (QHR) standards. One major difficulty with QHR devices based on EG is that their electrical properties drift slowly over time if the device is stored in air due to adsorption of atmospheric molecular dopants. The crucial parameter for device stability is the charge carrier density, which helps determine the magnetic flux density required for precise QHR measurements. This work presents one solution to this problem of instability in air by functionalizing the surface of EG devices with chromium tricarbonyl -Cr(CO) 3 . Observations of carrier density stability in air over the course of one year are reported, as well as the ability to tune the carrier density by annealing the devices. For low temperature annealing, the presence of Cr(CO) 3 stabilizes the electrical properties and allows for the reversible tuning of the carrier density in millimeter-scale graphene devices close to the Dirac point. Precision measurements in the quantum Hall regime show no detrimental effect on the carrier mobility., Competing Interests: Commercial equipment, instruments, and materials are identified in this paper in order to specify the experimental procedure adequately. Such identification is not intended to imply recommendation or endorsement by the National Institute of Standards and Technology or the United States government, nor is it intended to imply that the materials or equipment identified are necessarily the best available for the purpose. The authors declare no competing interests.

In this paper, we show that quantum Hall resistance measurements using two terminals may be as precise as four-terminal measurements when applying superconducting split contacts. The described sample designs eliminate resistance contributions of terminals and contacts such that the size and complexity of next-generation quantized Hall resistance devices can be significantly improved.