This companion guide revises and expands upon the established technical guidelines for reliable direct current measurements of the quantized Hall resistance, adapting them to the unique characteristics of epitaxial graphene. Graphene has emerged as a viable alternative to traditional Gallium Arsenide heterostructures for metrological applications due to its relaxed operating conditions. These less demanding requirements facilitate the use of low-cost, compact cryomagnet platforms, which is expected to broaden the deployment of primary resistance standards to National Metrology Institutes and other laboratories with limited resources. The guide explores the specific challenges and considerations of epitaxial graphene devices, including aspects of device choice, cooling and handling, contact resistance, conditions of quantization, and general measurements of the quantized Hall resistance. The presented details should assist those seeking to conduct rigorous characterization procedures to verify device integrity, ultimately contributing to a global effort to formally accept graphene-based devices as reliable primary resistance standards.

Quantum electrical metrology is an important application of collective states of matter. One prominent example is the quantum Hall condensate, which is essential for the realization of the resistance unit, the ohm. In graphene, the linear energy-momentum dispersion of quasiparticles allows for a practical realization of the quantum Hall resistance standard under easily accessible experimental conditions of temperature and magnetic field. With the maturity of technology, epitaxial graphene devices are now gradually deployed for primary resistance quantum standards at national metrology institutes. Here, we present the latest advances and future perspectives of graphene-based quantum electrical metrology, highlighting how this material can not only improve the realization conditions for the quantum resistance standard but also extend quantum-accurate realization of the ohm for the betterment of impedance and current metrology.

Producing large-area single-crystalline graphene is key to realizing its full potential in advanced applications, including twistronics. Yet, controlling graphene growth kinetics to avoid grain boundaries or multilayer growth remains challenging. Here, we demonstrate the possibility to obtain single-crystalline graphene free of multilayer domains via a facile one-step delamination of epitaxial graphene from silicon carbide (SiC). We find that this is enabled by a specific surface reconstruction of 4H-SiC(0001) that we achieve under our growth conditions. The high crystalline quality of graphene after delamination and transfer from the SiC substrate is confirmed by the observation of key fingerprints of Dirac fermions in quantum transport: ambipolar charge transport, Shubnikov–de Haas oscillations up to filling factor ν=4N+2=74, with N the Landau index, Berry phase of π, and half-integer quantum Hall effect in cm-sized crystals. The scalability of our process, explored with recycled 4”-SiC wafers, represents an advance toward large-scale integration of high-performance graphene applications.

The redefinition of the SI in 2019 cemented the importance of quantum metrology for the metric system. This is especially true for resistance metrology, which uses the quantum Hall effect (QHE) to realize the ohm. Together with the Josephson effect, these two quantum phenomena can be used to defined all other electrical units (e.g. ampere). Furthermore, electrical units such as ohm are also needed to realize the kilogram via the Kibble balance. The use of QHE for resistance metrology has existed for decades, but it has been relegated to advanced laboratories due to the stringent requirements on operating conditions (e.g. low temperatures, high magnetic fields). Recent advances in material science have shown that graphene can allow for operations under more relaxed conditions, opening up new applications. Calibrations against a primary quantum Hall resistance (QHR) standard can now be performed closer to the end-user, thereby shortening the calibration chain and reducing uncertainties. However, one practical limitation that still prevents widespread use of QHR in industry is that the resistance value of a single graphene QHR standard is limited to a single value close to 12.9 kOhm. For general use, decade values of resistance such as 100 Ohm, 1 kOhm, 10 kOhm etc. are much more desirable. One way to achieve flexibility in resistance values for QHR standards is to combine several units into arrays. Quantum Hall array resistance standards (QHARS) are an idea that has existed from the very beginning, but it has been challenging to achieve the desired metrological performance in practice. In order to be able to cover a wide range of resistance values, tens or hundreds of array elements need to be connected. Since each additional element represents a compounding chance of defects, the creation of QHARS demands flawless fabrication techniques in order to yield devices capable of performing with an accuracy on the order of part-per-billion (comparable to single QHR standards). Multiple technological advances from all over the world have paved the way for the creation of modern day graphene QHARS: Production of extremely high quality mono-crystalline epitaxial graphene on silicon carbide. Multi-terminal connections are used in order to reduce the influence of contact resistance. Superconducting leads are used to eliminate lead resistance and simplify connection schemes. Chemical doping is used to ensure homogeneous carrier density control of graphene. Pseudo-edge contact geometry is used to reliably create electrical contacts to graphene. All of which contributed to the work presented herein. RISE can now produce the largest, most complex, and most accurate graphene QHARS to date. The beneficial applications of QHARS are many. They can be used to improve resistance calibrations since a wide range of values can be calibrated directly against QHARS without the need for intermediate steps. Furthermore, arrays can be used to improve the realization of the ampere by combining them with Josephson arrays (voltage standards) Via Ohm's law, a wide range of currents can be generated. Finally, QHARS can be used to eliminate the need for artefact standards in the Kibble balance.

Producing large-area single-crystalline graphene is key to realizing its full potential in advanced applications, including twistronics. Yet, controlling graphene growth kinetics to avoid grain boundaries or multilayer growth remains challenging. Here, we demonstrate single-crystalline graphene free from multilayer domains via one-step delamination of epitaxial graphene from silicon carbide (SiC). This is enabled by a specific surface reconstruction of 4H-SiC(0001) achieved in our growth conditions. High crystalline quality is confirmed by the observation of the half-integer quantum Hall effect – the hallmark of monolayer graphene – in near cm-sized crystals. The scalability of our process, explored with 4”-wafers, represents an advance toward large-scale integration of high-performance graphene applications.

We report the lowest recorded levels of 1/f noise for graphene-based devices, at the level of SV/V2=SI/I2=4.4×10−16 (1/Hz), measured at f = 10 Hz (SV/V2=SI/I2 < 10−16 1/Hz for f > 100 Hz) in large-area epitaxial graphene on silicon carbide (epigraphene) Hall sensors. This performance is made possible through the combination of high material quality, low contact resistance achieved by edge contact fabrication process, homogeneous doping, and stable passivation of the graphene layer. Our study explores the nature of 1/f noise as a function of carrier density and device geometry and includes data from Hall sensors with device area range spanning over six orders of magnitude, with characteristic device length ranging from L = 1 μm to 1 mm. In optimized graphene Hall sensors, we demonstrate arrays to be a viable route to improve further the magnetic field detection: a simple parallel connection of two devices displays record-high magnetic field sensitivity at room temperature, with minimum detectable magnetic field levels down to Bmin = 9.5 nT/√Hz. The remarkable low levels of 1/f noise observed in epigraphene devices hold immense capacity for the design and fabrication of scalable epigraphene-based sensors with exceptional performance.

We describe the preliminary measurement conducted to establish a baseline dataset toward a cryogen-free system for quantized Hall resistance (QHR) standard application. This paper illustrates the current state-of-the-art cryogenic system, the quantization verification and ratio measurement between an established GaAs Hall bar and a graphene-base quantum Hall array resistance standard (GQHARS). The technology comparison is carried out with a room temperature ratio bridge.

We present the first steps taken towards a graphene quantum Hall effect ac resistance standard at RISE. A new measurement setup has been developed including a graphene quantum Hall effect device suitable for the kilohertz range and a coaxial cryoprobe to be used together with a coaxial impedance bridge based on inductive voltage dividers. 1:1 ratio resistance measurements of the graphene device against a 12.9 k Omega ac resistance standard resulted in a linear frequency dependent (approximate to 0.2 (mu O/O)/kHz) deviation from the quantized dc value.

The paper reports a results of series of interlaboratory comparisons of low impedance measurements at frequencies relevant for electrochemical impedance spectroscopy (EIS) of commercial lithium-ion cells. Two comparisons are presented. The first, bilateral comparison has focused on low impedance standards calibration in a full complex plane using digital sampling setups. The second comparison has focused on calibration and use of commercial 4-terminal battery EIS meters. Both comparisons have covered the impedance range from 50μ℧ to 100m℧ across the full complex plane in a frequency range from 0.01Hz up to 5kHz. Finally, the paper summarizes practices identified as critical for achieving measurement compatibility among various labs.

In this work we investigate the long-term stability of epitaxial graphene (epigraphene) quantum Hall resistance standards, including single devices and an array device composed of 236 elements providing R K /236 ≈ 109 Ω, with R K the von Klitzing constant. All devices utilize the established technique of chemical doping via molecular dopants to achieve homogenous doping and control over carrier density. However, optimal storage conditions and the long-term stability of molecular dopants for metrological applications have not been widely studied. In this work we aim to identify simple storage techniques that use readily available and cost-effective materials which provide long-term stability for devices without the need for advanced laboratory equipment. The devices are stored in glass bottles with four different environments: ambient, oxygen absorber, silica gel desiccant, and oxygen absorber/desiccant mixture. We have tracked the carrier densities, mobilities, and quantization accuracies of eight different epigraphene quantum Hall chips for over two years. We observe the highest stability (i.e. lowest change in carrier density) for samples stored in oxygen absorber/desiccant mixture, with a relative change in carrier density below 0.01% per day and no discernable degradation of quantization accuracy at the part-per-billion level. This storage technique yields a comparable stability to the currently established best storage method of inert nitrogen atmosphere, but it is much easier to realize in practice. It is possible to further optimize the mixture of oxygen absorber/desiccant for even greater stability performance in the future. We foresee that this technique can allow for simple and stable long-term storage of polymer-encapsulated molecular doped epigraphene quantum Hall standards, removing another barrier for their wide-spread use in practical metrology.

We present a fabrication method for reliably and reproducibly forming electrical contacts to 2D materials, based on the tri-layer resist system. We demonstrate the applicability of this method for epitaxial graphene on silicon carbide (epigraphene) and the transition metal dichalcogenides (TMDCs) molybdenum disulfide ($MoS_2$). For epigraphene, the specific contact resistances are of the order of $\rho_c$ ~ $50$ $\Omega\mu m$, and follow the Landauer quantum limit, $\rho_c \propto n^{-1/2}$, with $n$ being the carrier density of graphene. For $MoS_2$ flakes, our edge contacts enable field effect transistors (FET) with ON/OFF ratio of $>10^6$ at room temperature ( $>10^9$ at cryogenic temperatures). The fabrication route here demonstrated allows for contact metallization using thermal evaporation and also by sputtering, giving an additional flexibility when designing electrical interfaces, which is key in practical devices and when exploring the electrical properties of emerging materials.

Graphene quantum Hall effect (QHE) resistance standards have the potential to provide superior realizations of three key units in the new International System of Units (SI): the ohm, the ampere, and the kilogram (Kibble Balance). However, these prospects require different resistance values than practically achievable in single graphene devices (~12.9 kΩ), and they need bias currents two orders of magnitude higher than typical breakdown currents IC ~ 100 μA. Here we present experiments on quantization accuracy of a 236-element quantum Hall array (QHA), demonstrating RK/236 ≈ 109 Ω with 0.2 part-per-billion (nΩ/Ω) accuracy with IC ≥ 5 mA (~1 nΩ/Ω accuracy for IC = 8.5 mA), using epitaxial graphene on silicon carbide (epigraphene). The array accuracy, comparable to the most precise universality tests of QHE, together with the scalability and reliability of this approach, pave the road for wider use of graphene in the new SI and beyond.

The paper reports an interlaboratory comparison of low impedance measurements at frequencies relevant for electrochemical impedance spectroscopy (EIS) of commercial lithium-ion cells.The comparisons cover an impedance range from 50 μΩ to 100 mΩ across the full complex plane in a frequency range 0.01 Hz up to 5 kHz.A first comparison covered calibration of low impedance standards by reference digital sampling impedance setups in 4-terminal and 4 terminal-pair connections.A second comparison used commercial 4-terminal EIS meters to measure the low impedance standards characterised in the first comparison.

We present a fabrication method for reliably and reproducibly forming electrical contacts to 2D materials, based on the tri-layer resist system. We demonstrate the applicability of this method for epitaxial graphene on silicon carbide (epigraphene) and the transition metal dichalcogenides (TMDCs) molybdenum disulfide (MoS_2). For epigraphene, the specific contact resistances are of the order of ρ_c 50 Ωμ m, and follow the Landauer quantum limit, ρ_c ∝ n^-1/2, with n being the carrier density of graphene. For MoS_2 flakes, our edge contacts enable field effect transistors (FET) with ON/OFF ratio of > 10^6 at room temperature ( > 10^9 at cryogenic temperatures). The fabrication route here demonstrated allows for contact metallization using thermal evaporation and also by sputtering, giving an additional flexibility when designing electrical interfaces, which is key in practical devices and when exploring the electrical properties of emerging materials.

We show that epitaxial graphene on silicon carbide (epigraphene) grown at high temperatures (T >1850 °C) readily acts as material for implementing solar-blind ultraviolet (UV) detectors with outstanding performance. We present centimeter-sized epigraphene metal–semiconductor–metal (MSM) detectors with a peak external quantum efficiency of η ∼ 85% for wavelengths λ = 250–280 nm, corresponding to nearly 100% internal quantum efficiency when accounting for reflection losses. Zero bias operation is possible in asymmetric devices, with the responsivity to UV remaining as high as R = 134 mA/W, making this a self-powered detector. The low dark currents Io ∼ 50 fA translate into an estimated record high specific detectivity D = 3.5 × 1015 Jones. The performance that we demonstrate, together with material reproducibility, renders epigraphene technologically attractive to implement high-performance planar MSM devices with a low processing effort, including multi-pixel UV sensor arrays, suitable for a number of practical applications.

The quantum Hall effect (QHE) is a cornerstone in the new International System of Units (SI), wherein the base units are derived from seven fundamental constants such as Planck's constant h and elementary charge e. Graphene has revolutionized practical resistance metrology by enabling the realization of quantized resistance h/2e^2 = 12.9... kOhm under relaxed experimental conditions. Looking ahead, graphene also has the potential to improve realizations of the electronic kilogram using the Kibble balance, and the quantum Ampere in wide current ranges. However, these prospects require different resistance values than practically achievable in single QHE devices, while also imposing stringent demands on energy dissipation in single QHE devices, ultimately requiring currents almost two orders of magnitude higher than the typical QHE breakdown currents IC ~ 100 uA achievable in graphene. Here we present unprecedented accuracy in the quantization of a record sized quantum Hall array (QHA), demonstrating RK/236 ~ 109 Ohm with 0.2 part-per-billion (nOhm/Ohm) accuracy with IC over 5 mA (~ 1 nOhm/Ohm accuracy for IC = 8.5 mA), using epitaxial graphene on silicon carbide (epigraphene). The array quantization accuracy, comparable to the most precise universality tests of QHE in single Hall bar devices, together with the scalability and reliability of this approach pave the road for superior realizations of three key units in the modern SI: the ohm, the ampere, and the kilogram.

We investigate the basic charge and heat transport properties of charge neutral epigraphene at sub-kelvin temperatures, demonstrating a nearly logarithmic dependence of electrical conductivity over more than two decades in temperature. Using graphene's sheet conductance as an in situ thermometer, we present a measurement of electron-phonon heat transport at mK temperatures and show that it obeys the T4 dependence characteristic for a clean two-dimensional conductor. Based on our measurement, we predict the noise-equivalent power of ∼10−22 W/Hz of the epigraphene bolometer at the low end of achievable temperatures.

We investigate the basic charge and heat transport properties of charge neutral epigraphene at sub-kelvin temperatures, demonstrating nearly logarithmic dependence of electrical conductivity over more than two decades in temperature. Using graphene's sheet conductance as in-situ thermometer, we present a measurement of electron-phonon heat transport at mK temperatures and show that it obeys the T^4 dependence characteristic for clean two-dimensional conductor. Based on our measurement we predict the noise-equivalent power of ∼ 10^-22 W/√( Hz) of epigraphene bolometer at the low end of achievable temperatures.

Boosting the sensitivity of solid‐state gas sensors by incorporating nanostructured materials as the active sensing element can be complicated by interfacial effects. Interfaces at nanoparticles, grains, or contacts may result in nonlinear current–voltage response, high electrical resistance, and ultimately, electric noise that limits the sensor read‐out. This work reports the possibility to prepare nominally one atom thin, electrically continuous platinum layers by physical vapor deposition on the carbon zero layer (also known as the buffer layer) grown epitaxially on silicon carbide. With a 3–4 Å thin Pt layer, the electrical conductivity of the metal is strongly modulated when interacting with chemical analytes, due to charges being transferred to/from Pt. The strong interaction with chemical species, together with the scalability of the material, enables the fabrication of chemiresistor devices for electrical read‐out of chemical species with sub part‐per‐billion (ppb) detection limits. The 2D system formed by atomically thin Pt on the carbon zero layer on SiC opens up a route for resilient and high sensitivity chemical detection, and can be the path for designing new heterogenous catalysts with superior activity and selectivity.

Epitaxial graphene on silicon carbide, or epigraphene, provides an excellent platform for Hall sensing devices in terms of both high electrical quality and scalability. However, the challenge in controlling its carrier density has thus far prevented systematic studies of epigraphene Hall sensor performance. In this work we investigate epigraphene Hall sensors where epigraphene is doped across the Dirac point using molecular doping. Depending on the carrier density, molecular-doped epigraphene Hall sensors reach room temperature sensitivities $S_V=0.23 V/VT$,$S_I=1440 V/AT$ and magnetic field detection limits down to $B_{MIN}=27$ $nT/\sqrt{Hz}$ at 20 kHz. Thermally stabilized devices demonstrate operation up to $T=150$ $^oC$ with $S_V=0.12 V/VT$, $S_I=300 V/AT$ and $B_{MIN}\approx 100$ $nT/\sqrt{Hz}$ at 20 kHz.