Quantum Resistance Standards Research Articles

A balanced quantum Hall resistor

The quantum anomalous Hall effect in magnetic topological insulators has potential for use in quantum resistance metrology applications. Electronic conductance is quantized to e2/h (where e is the elementary charge and h is the Planck constant) due to the effect, which persists down to zero external magnetic field and is compatible with the quantum standard of voltage. However, metrological applications of the quantum anomalous Hall effect are currently restricted by the need for low measurement currents and low temperatures. Here we report a measurement scheme that increases the robustness of a zero-magnetic-field quantum anomalous Hall resistor and extends its operating range to higher currents. In the scheme, we simultaneously inject current into two disconnected perimeters of a multi-terminal Corbino device, which is based on V0.1(Bi0.2Sb0.8)1.9Te3, to balance the electrochemical potential between the edges. This screens the electric field that drives backscattering through the bulk and thus improves the stability of the quantization at increased currents. Our approach could also be applied to existing quantum resistance standards that rely on the integer quantum Hall effect.

On the calibration of DC resistance ratio bridges

Current comparator bridges are employed for the realization of the resistance scale from the quantum Hall effect in several National Metrology Institutes and calibration centers. Quantum resistance standards under development, based on novel materials and tabletop dry cryostats, make the more achievable DC current comparator bridges (DCCs) a viable alternative to the more accurate but more expensive cryogenic current comparator bridges (CCCs). A DCC ratios’ calibration against a reference CCC is a straightforward way to improve the DCC’s performances and the resistance scale overall accuracy.The paper reports the calibration results of two DCCs on the ratios employed in a 1Ω to 10kΩ resistance scale traceable to a 12.906kΩ quantized Hall resistance, showing a good reproducibility and stability of the DCC readings over the measurement period and supporting the possibility of a DCC errors’ correction and of a realization of the primary resistance scale at the 10-8 level.

Improvements of the programmable quantum current generator for better traceability of electrical current measurements

A programmable quantum current generator based on the application of Ohm’s law to quantum voltage and resistance standards has demonstrated a realization of the ampere from the elementary charge with a 10−8 relative uncertainty (Brun-Picard et al 2016 Phys. Rev. X 6 041051). Here, we report on improvements of the device leading to a noise reduction of the generated quantized current. The improved quantum current generator is used to calibrate different ammeters with lower measurement uncertainties. Besides, measurements of its quantized current using a calibrated ultrastable low-noise current amplifier have shown that the realizations of the ampere at PTB (Physikalisch-Technische Bundesanstalt) and LNE (Laboratoire national de Métrologie et d’essais) in the range ±50 μA agreed to −3.7 parts in 107 with a combined standard uncertainty of 3.1 parts in 107 (coverage factor k c = 1).

Towards epitaxial graphene p-n junctions as electrically programmable quantum resistance standards

We report the fabrication and measurement of top gated epitaxial graphene p-n junctions where exfoliated hexagonal boron nitride (h-BN) is used as the gate dielectric. The four-terminal longitudinal resistance across a single junction is well quantized at the von Klitzing constant {{boldsymbol{R}}}_{{boldsymbol{K}}} with a relative uncertainty of 10−7. After the exploration of numerous parameter spaces, we summarize the conditions upon which these devices could function as potential resistance standards. Furthermore, we offer designs of programmable electrical resistance standards over six orders of magnitude by using external gating.

Circuit models and SPICE macro-models for quantum Hall effect devices

Precise electrical measurement technology based on the quantum Hall effect is one of the pillars of modern quantum electrical metrology. Electrical networks including one or more QHE elements can be used as quantum resistance and impedance standards. The analysis of these networks allows metrologists to evaluate the effect of the inevitable parasitic parameters on their performance as standards. This paper presents a concise review of the various circuit models for QHE elements proposed in the literature, and the development of a new model. This last model is particularly suited to be employed with the analogue electronic circuit simulator SPICE. The SPICE macro-model and examples of SPICE simulations, validated by comparison with the corresponding analytical solution and/or experimental data, are provided.

Quantum resistance standard accuracy close to the zero-dissipation state

We report on a comparison of four GaAs/AlGaAs-based quantum resistance standards using an original technique adapted from the well-known Wheatstone bridge. This work shows that the quantized Hall resistance at Landau level filling factor ν=2 can be reproducible with a relative uncertainty of 32×10−12 in the dissipationless limit of the quantum Hall effect regime. In the presence of a very small dissipation characterized by a mean macroscopic longitudinal resistivity Rxx(B)¯ of a few μΩ, the discrepancy ΔRH(B) between quantum Hall resistors measured on the Hall plateau at magnetic induction B turns out to follow the so-called resistivity rule Rxx(B)¯=αB×d(ΔRH(B))/dB. While the dissipation increases with the measurement current value, the coefficient α stays constant in the range investigated (40−120 μA). This result enlightens the impact of the dissipation emergence in the two-dimensional electron gas on the Hall resistance quantization, which is of major interest for the resistance metrology. The quantum Hall effect is used to realize a universal resistance standard only linked to the electron charge e and the Planck constant h and it is known to play a central role in the upcoming revised Système International of units. There are therefore fundamental and practical benefits in testing the reproducibility property of the quantum Hall effect with better and better accuracy.

Precision quantization of Hall resistance in transferred graphene

We show that quantum resistance standards made of transferred graphene reach the uncertainty of semiconductor devices, the current reference system in metrology. A large graphene device (150 × 30 μm2), exfoliated and transferred onto GaAs revealed a quantization with a precision of ( − 5.1 ± 6.3) · 10−9 accompanied by a vanishing longitudinal resistance at current levels exceeding 10 μA. While such performance had previously only been achieved with epitaxially grown graphene, our experiments demonstrate that transfer steps, inevitable for exfoliated graphene or graphene grown by chemical vapor deposition, are compatible with the requirements of high quality quantum resistance standards.

Quantum resistance standards with double 2deg

We have developed a new generation of quantum Hall array resistance standards (QHARS) obtained from GaAs/AlGaAs heterostructures with double two-dimensional electron gases (2DEGs) grown by the metal-organic vapor phase epitaxy process. We have achieved the fabrication of such a multilayer system with well matched carrier density and mobility of the two 2DEGs and characteristics required for metrological use. This technological achievement allowed calibrations in terms of a quantized Hall resistance (R/sub K//2 on i=2 plateau) of a single Hall bar (R/sub K//4) and 50 Hall bars placed in parallel by triple connections QHARS129 (R/sub K//200). In both cases relative deviations of their Hall resistance from their expected nominal value are found lower than eight parts in 10/sup 9/, corresponding to the measurement uncertainty (1/spl sigma/). These measurements were performed on QHARS129 samples supplied by higher measuring currents up to 2 mA at 1.3 K.