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The new definition of the ampere calls for a quantum current standard able to deliver a flow of elementary charges per second controlled with a relative uncertainty of one part in $10^8$. Despite many efforts, nanodevices handling electrons one by one have never been able to demonstrate such an accuracy. The alternative route based on applying Ohm's law to the Josephson voltage and quantum Hall standards recently reached the target uncertainty but this was at the expense of the application of error corrections, hampering simplicity and further improvement. As a result, national metrology institutes still lack an operational quantum current standard. Here, we present a new quantum current generator, combining both quantum standards and a superconducting cryogenic amplifier, free of error correction, which provides quantized currents driven by the Josephson microwave signal. We show that it can realize the ampere definition with the target uncertainty over a range extended from mA down to $\mu$A and improve end-user current measurements, which are up to now a hundred times less accurate. Other prospects include measuring large resistances using the new current standard in conjunction with a quantum voltmeter and, by exploiting its low-noise performances, bridging the gap with the lower currents of other quantum current sources., Comment: 6 pages, 5 figures, Methods, 6 Extended Data figures, 3 Extended Data Tables

A new resistance bridge has been built at the Laboratoire national de m\'etrologie et d'essais (LNE) to improve the ohm realization in the $Syst\`eme International$ (SI) of units from the quantum Hall effect. We describe the instrument, the performance of which relies on two synchronized and noise-filtered current sources, an accurate and stable current divider and a cryogenic current comparator (CCC) having a low noise of $\mathrm{80~pA.t/Hz^{1/2}}$. The uncertainty budget for the measurement of the 100 $\Omega/(R_\mathrm{K}/2)$ ratio, where $R_\mathrm{K}$ is the von Klitzing constant, amounts to a few parts in $10^{10}$ only., Comment: 14 pages, 16 figures, Accepted in IEEE. Trans. Instrum. Meas

By fixing two fundamental constants from quantum mechanics, the Planck constant $h$ and the elementary charge $e$, the revised Syst\`eme International (SI) of units endorses explicitly quantum mechanics. This evolution also highlights the importance of this theory which underpins the most accurate realization of the units. From 20 May 2019, the new definitions of the kilogram and of the ampere, based on fixed values of $h$ and $e$ respectively, will particularly impact the electrical metrology. The Josephson effect (JE) and the quantum Hall effect (QHE), used to maintain voltage and resistance standards with unprecedented reproducibility since 1990, will henceforth provide realizations of the volt and the ohm without the uncertainties inherited from the older electromechanical definitions. More broadly, the revised SI will sustain the exploitation of quantum effects to realize electrical units, to the benefit of end-users. Here, we review the state-of-the-art of these standards and discuss further applications and perspectives., Comment: 78 pages, 35 figures

One major change of the future revision of the International System of Units (SI) is a new definition of the ampere based on the elementary charge \emph{e}. Replacing the former definition based on Amp\`ere's force law will allow one to fully benefit from quantum physics to realize the ampere. However, a quantum realization of the ampere from \emph{e}, accurate to within $10^{-8}$ in relative value and fulfilling traceability needs, is still missing despite many efforts have been spent for the development of single-electron tunneling devices. Starting again with Ohm's law, applied here in a quantum circuit combining the quantum Hall resistance and Josephson voltage standards with a superconducting cryogenic amplifier, we report on a practical and universal programmable quantum current generator. We demonstrate that currents generated in the milliampere range are quantized in terms of $ef_\mathrm{J}$ ($f_\mathrm{J}$ is the Josephson frequency) with a measurement uncertainty of $10^{-8}$. This new quantum current source, able to deliver such accurate currents down to the microampere range, can greatly improve the current measurement traceability, as demonstrated with the calibrations of digital ammeters. Beyond, it opens the way to further developments in metrology and in fundamental physics, such as a quantum multimeter or new accurate comparisons to single electron pumps., Comment: 15 pages, 4 figures

The quantum Hall effect (QHE) theoretically provides a universal standard of electrical resistance in terms of the Planck constant $h$ and the electron charge $e$. In graphene, the spacing between the lowest discrete energy levels occupied by the charge carriers under magnetic field is exceptionally large. This is promising for a quantum Hall resistance standard more practical in graphene than in the GaAs/AlGaAs devices currently used in national metrology institutes. Here, we demonstrate that large QHE devices, made of high quality graphene grown by propane/hydrogen chemical vapour deposition on SiC substrates, can surpass state-of-the-art GaAs/AlGaAs devices by considerable margins in their required operational conditions. In particular, in the device presented here, the Hall resistance is accurately quantized within $1\times 10^{-9}$ over a 10-T wide range of magnetic field with a remarkable lower bound at 3.5 T, temperatures as high as 10 K, or measurement currents as high as 0.5 mA. These significantly enlarged and relaxed operational conditions, with a very convenient compromise of 5 T, 5.1 K and 50 $\mu$A, set the superiority of graphene for this application and for the new generation of versatile and user-friendly quantum standards, compatible with a broader industrial use. We also measured an agreement of the quantized Hall resistance in graphene and GaAs/AlGaAs with an ultimate relative uncertainty of $8.2\times 10^{-11}$. This supports the universality of the QHE and its theoretical relation to $h$ and $e$, essential for the application in metrology, particularly in view of the forthcoming Syst\`eme International d'unit\'es (SI) based on fundamental constants of physics, including the redefinition of the kilogram in terms of $h$., Comment: 33 pages (Main Text pp. 1-17 with 6 figures; Supplementary Materials pp. 18-33 with 8 figures)

Replacing GaAs by graphene to realize more practical quantum Hall resistance standards (QHRS), accurate to within $10^{-9}$ in relative value, but operating at lower magnetic fields than 10 T, is an ongoing goal in metrology. To date, the required accuracy has been reported, only few times, in graphene grown on SiC by sublimation of Si, under higher magnetic fields. Here, we report on a device made of graphene grown by chemical vapour deposition on SiC which demonstrates such accuracies of the Hall resistance from 10 T up to 19 T at 1.4 K. This is explained by a quantum Hall effect with low dissipation, resulting from strongly localized bulk states at the magnetic length scale, over a wide magnetic field range. Our results show that graphene-based QHRS can replace their GaAs counterparts by operating in as-convenient cryomagnetic conditions, but over an extended magnetic field range. They rely on a promising hybrid and scalable growth method and a fabrication process achieving low-electron density devices., Comment: 12 pages, 8 figures

We report on the observation of strong backscattering of charge carriers in the quantum Hall regime of polycrystalline graphene grown by chemical vapor deposition, which alters the accuracy of the Hall resistance quantization. The temperature and magnetic field dependence of the longitudinal conductivity exhibits unexpectedly smooth power law behaviors, which are incompatible with a description in terms of variable range hopping or thermal activation, but rather suggest the existence of extended or poorly localized states at energies between Landau levels. Such states could be caused by the high density of line defects (grain boundaries and wrinkles) that cross the Hall bars, as revealed by structural characterizations. Numerical calculations confirm that quasi-one-dimensional extended non-chiral states can form along such line defects and short-circuit the Hall bar chiral edge states., Comment: 9 pages, 10 figures

We investigate the magneto-transport properties of epitaxial graphene single-layer on 4H-SiC(0001), grown by atmospheric pressure graphitization in Ar, followed by H2 intercalation. We directly demonstrate the importance of saturating the Si dangling bonds at the graphene/SiC(0001) interface to achieve high carrier mobility. Upon successful Si dangling bonds elimination, carrier mobility increases from 3 000 cm^2/Vs to > 11 000 cm^2/Vs at 0.3 K. Additionally, graphene electron concentration tends to decrease from a few 10^12 cm^-2 to less than 10^12 cm^-2. For a typical large (30x280 um^2) Hall bar, we report the observation of the integer quantum Hall states at 0.3 K with well developed transversal resistance plateaus at Landau level fillings factors of nu = 2, 6, 10, 14.. 42 and Shubnikov de Haas oscillation of the longitudinal resistivity observed from about 1 T. In such a device, the Hall state quantization at nu=2, at 19 T and 0.3 K, can be very robust: the dissipation in electronic transport can stay very low, with the longitudinal resistivity lower than 5 mOhm, for measurement currents as high as 250 uA. This is very promising in the view of an application in metrology.

We propose a way to realize a programmable quantum current standard (PQCS) from the Josephson voltage standard and the quantum Hall resistance standard (QHR) exploiting the multiple connection technique provided by the quantum Hall effect (QHE) and the exactness of the cryogenic current comparator. The PQCS could lead to breakthroughs in electrical metrology like the realization of a programmable quantum current source, a quantum ampere-meter and a simplified closure of the Quantum Metrological Triangle. Moreover, very accurate universality tests of the QHE could be performed by comparing PQCS based on different QHRs., Comment: 5 pages, 5 figures

In this letter we report on transport measurements of epitaxial graphene on SiC(0001) with oxygen adsorption. In a $50\times 50 \mu\mathrm{m^2}$ size Hall bar we observe the half-integer quantum Hall effect with a transverse resistance plateau quantized at filling factor around $\nu = 2$, an evidence of monolayer graphene. We find low electron concentration of $9\times 10^{11} \textrm{cm}^{-2}$ and we show that a doping of $10^{13}\textrm{cm}^{-2}$ which is characteristic of intrinsic epitaxial graphene can be restored by vacuum annealing. The effect of oxygen adsorption on carrier density is confirmed by local angle-resolved photoemission spectroscopy measurements. These results are important for understanding oxygen adsorption on epitaxial graphene and for its application to metrology and mesoscopic physics where a low carrier concentration is required., Comment: 4 pages, 3 figures

Metrological investigations of the quantum Hall effect (QHE) completed by transport measurements at low magnetic field are carried out in a-few-$\mu\mathrm{m}$-wide Hall bars made of monolayer (ML) or bilayer (BL) exfoliated graphene transferred on $\textrm{Si/SiO}_{2}$ substrate. From the charge carrier density dependence of the conductivity and from the measurement of the quantum corrections at low magnetic field, we deduce that transport properties in these devices are mainly governed by the Coulomb interaction of carriers with a large concentration of charged impurities. In the QHE regime, at high magnetic field and low temperature ($T<1.3 \textrm{K}$), the Hall resistance is measured by comparison with a GaAs based quantum resistance standard using a cryogenic current comparator. In the low dissipation limit, it is found quantized within 5 parts in $10^{7}$ (one standard deviation, $1 \sigma$) at the expected rational fractions of the von Klitzing constant, respectively $R_{\mathrm{K}}/2$ and $R_{\mathrm{K}}/4$ in the ML and BL devices. These results constitute the most accurate QHE quantization tests to date in monolayer and bilayer exfoliated graphene. It turns out that a main limitation to the quantization accuracy, which is found well above the $10^{-9}$ accuracy usually achieved in GaAs, is the low value of the QHE breakdown current being no more than $1 \mu\mathrm{A}$. The current dependence of the longitudinal conductivity investigated in the BL Hall bar shows that dissipation occurs through quasi-elastic inter-Landau level scattering, assisted by large local electric fields. We propose that charged impurities are responsible for an enhancement of such inter-Landau level transition rate and cause small breakdown currents., Comment: 14 pages, 9 figures

Our study presents experimental measurements of the contact and longitudinal voltage drops in Hall bars, as a function of the current amplitude. We are interested in the heating phenomenon which takes place before the breakdown of the quantum Hall effect, i.e. the pre-breakdown regime. Two types of samples has been investigated, at low temperature (4.2 and 1.5K) and high magnetic field (up to 13 T). The Hall bars have several different widths, and our observations clearly demonstrate that the size of the sample influences the heating phenomenon. By measuring the critical currents of both contact and longitudinal voltages, as a function of the filling factor (around $i=2$), we highlight the presence of a high electric field domain near the source contact, which is observable only in samples whose width is smaller than 400 microns., Comment: 4 pages, 5 igures, 7th International Symposium of Research in High Magnetic Fields, to be published in physica B

This paper reports on an experimental study of the contact resistance of Hall bars in the Quantum Hall Effect regime while increasing the current through the sample. These measurements involve also the longitudinal resistance and they have been always performed before the breakdown of the Quantum Hall Effect. Our investigations are restricted to the $i=2$ plateau which is used in all metrological measurements of the von Klitzing constant $R_K$. A particular care has been taken concerning the configuration of the measurement. Four configurations were used for each Hall bar by reversing the current and the magnetic field polarities. Several samples with different width have been studied and we observed that the critical current for the contact resistance increases with the width of the Hall bar as previously observed for the critical current of the longitudinal resistance. The critical currents exhibit either a linear or a sublinear increase. All our observations are interpreted in the current understanding of the Quantum hall effect brekdown. Our analysis suggests that a heated region appears at the current contact, develops and then extends in the whole sample while increasing the current. Consequently, we propose to use the contact resistance as an electronic thermometer for the Hall fluid., Comment: 27 pages, 14 figures, resubmitted to phys. Rev. B

It is theoretically possible to combine several Hall bars in arrays to define new quantum standards with perfectly quantized resistance values. We have thus, for the first time, developed and fabricated novel Quantum Hall Array Resistance Standards (QHARS) made of a large number N (N=100, 50) of Hall bars placed in parallel using a triple connections technique. The Hall resistance of these quantum standards is found to be very well quantized. On the i=2 Hall plateau, the resistance of specific good arrays stays equal to RK/2N within 5 parts in 10^9 for supplying currents up to 2 mA at a 1.3 K temperature. The mean longitudinal resistance of the Hall bars which constitute the arrays has been determined through the analysis of the array equivalent electrical circuit. This measurement shows that the carrier transport in the Hall bars is dissipation-less. This work therefore demonstrates the efficiency of the multiple connections technique and consequently that QHARS are likely to extend the QHE metrological applications., Comment: 10 pages, PDF file, accepted in J. Appl. Phys

We study the transport through gated GaAS:Si wires of 0.5 micrometer length in the insulating regime and observe transport via elastic tunneling at very low temperature. We describe the mean positive magnetoconductance and the mesoscopic fluctuations of the conductance (versus energy or magnetic field) purely within one electron model without introducing Coulomb blockade considerations., Comment: 23 pages, 19 figures

We observe an inversion of the low temperature dependence for the conductivity of doped GaAs by application of a magnetic field. This inversion happens when Wct = 1, as predicted by Houghton (PRB25, 2196, 1982) for the correction to conductivity due to screened Coulomb repulsion in the diffusive regime. This correction follows the oscillating behavior of the transport elastic time entering the Shubnikov-de Haas regime. For Wct > 1, we observe that the Hartree part of the interaction correction is suppressed. Moreover, the total correction seems strongly reduced although its dependence stays logarithmic., Comment: 4 pages, 4 figures