In the revised International System of Units (SI), the ohm and the volt are realized from the von Klitzing constant and the Josephson constant, and a practical realization of the ampere is possible by applying Ohm’s law directly to the quantum Hall and Josephson effects. As a result, it is possible to create an instrument capable of realizing all three primary electrical units, but the development of such a system remains challenging. Here we report a unified realization of the volt, ohm and ampere by integrating a quantum anomalous Hall resistor (QAHR) and a programmable Josephson voltage standard (PJVS) in a single cryostat. Our system has a quantum voltage output that ranges from 0.24 mV to 6.5 mV with combined relative uncertainties down to 3 μV V−1. The QAHR provides a realization of the ohm at zero magnetic field with uncertainties near 1 μΩ Ω−1. We use the QAHR to convert a longitudinal current to a quantized Hall voltage and then directly compare that against the PJVS to realize the ampere. We determine currents in the range of 9.33–252 nA, and our lowest uncertainty is 4.3 μA A−1 at 83.9 nA. For other current values, a systematic error that ranges from −10 μA A−1 to −30 μA A−1 is present due to the imperfect isolation of the PJVS microwave bias. A unified realization of the volt, ohm and ampere can be achieved by integrating a quantum anomalous Hall resistor and a programmable Josephson voltage standard in a single cryostat.

A 1G Omega star-mesh quantized Hall array resistance standard (QHARS) assembled from 37 individual elements, each exhibiting the quantum Hall effect (QHE), was fabricated and tested. The 1G Omega QHARS has three orders of magnitude fewer elements than a largely series 1G Omega QHARS, which would require approximately 77480 elements. A dual source bridge (DSB), using a nanovolt detector and a modified algorithm using least-squares analysis was used to interpolate a bridge null from five measurement points taken near the null of the linear measurement system. The 1G Omega star-mesh QHARS was used as a standard to calibrate 100 M Omega , 1G Omega , and 10 G Omega high resistance standards. The star-mesh measurements agreed within the combined standard uncertainties of the values of these standards based on traditional high resistance scaling from the i=2 quantized Hall resistance value of 12906.4037...Omega , where guarded Hamon transfer standards and DSBs are used to build-up to high resistance ranges from 1 M Omega standard resistors.

The scaling theory of Anderson localization provides a comprehensive framework for understanding the transition between the localized and the extended states near the quantum Hall (QH) regime. Prior studies or measurements of the inelastic scattering exponent p in two dimensions, which plays a crucial role in quantum dephasing, mostly extract a magnetic-field-independent p spanning a wide range (1 <= p <= 4) or determine p indirectly through the relation p = 2 kappa gamma. Here kappa and gamma are the critical exponent and the universal exponent, respectively. Therefore, it is highly desirable to measure p at different magnetic fields directly. Here, we study two different types of graphene devices over a wide range of magnetic fields in both the low and high current regimes. The latter allows us to determine p directly through the current-heating model. We show thatp ti 2 using current-heating studies in all cases. At high fields, these results are in excellent agreement with that determined from p = 2 kappa gamma in the low current regime. However, with low currents, a vastly different inelastic scattering exponent p' ti 1 is found in our analysis of weak localization (WL) in the low-field region. Such an unexpected discrepancy may be explained as follows. In the WL analysis, the electron and phonon systems are in thermal equilibrium so that we probe p' ti 1. In contrast, in the high current regime where there is a substantial difference between the electron effective temperature and the lattice (phonon) temperature, we extract the exponentp ti 2. Our new experimental results further add mysteries to the seemly well-understood QH systems and quantum dephasing in two dimensions.

The quantum Hall (QH) effect is one of the most widely studied physical phenomenon in two dimensions. The plateau-plateau transition within this effect can be comprehensively described by the scaling theory, which encompasses three pivotal exponents: the critical exponent κ, the inelastic scattering exponent p, and the universal exponent γ. Prior studies have focused on measuring κ and estimating γ, assuming a constant p value of 2 across magnetic fields. Here, our work marks a significant advancement by measuring all three exponents within a single graphene device and a conventional two-dimensional electron system. This study uniquely determines p at low magnetic fields (weak localization region and well outside the QH regime) and high magnetic fields (in the vicinity of the QH regime). Employing a comprehensive analytical approach that includes weak localization, plateau-plateau transitions, and variable range hopping, we have directly determined κ, p, and γ. Our findings reveal a distinct variation in p, shifting from 1 in the low magnetic field regime to 2 in the QH regime in graphene.

A recent mathematical framework for optimizing resistor networks to achieve values in the MO through GO levels was employed for two specific cases. Objectives here include proof of concept and identification of possible apparatus limitations for future experiments involving graphene-based quantum Hall array resistance standards. Using fractal-like, or recursive, features of the framework allows one to calculate and implement network designs with substantially lower-valued resistors. The cases of 100 M Omega and 1 G Omega demonstrate that, theoretically, one would not need more than 100 quantum Hall elements to achieve these high resistances.

This paper describes the characterization of the quantum anomalous Hall (QAH) effect resistor with Chromium-doped Bismuth Antimony Telluride with the efforts in coupling directly to a programmable Josephson voltage standard (PJVS) at zero magnetic field. The precision measurement of the QAH resistance was performed under the presence of microwave signal biased to the PJVS. Understanding such effect will help to improve the experimental set-up for integrating multiple quantum electrical standards in a single system.

A recent mathematical framework for optimizing resistor networks to achieve values in the MΩ through GΩ levels was employed for two specific cases. Objectives here include proof of concept and identification of possible apparatus limitations for future experiments involving graphene-based quantum Hall array resistance standards. Using fractal-like, or recursive, features of the framework allows one to calculate and implement network designs with substantially lower-valued resistors. The cases of 100 MΩ and 1 GΩ demonstrate that, theoretically, one would not need more than 100 quantum Hall elements to achieve these high resistances.

Theoretically wye-delta transformation can be used to realize ultra-high resistances up to PO. For graphene-based quantum Hall array resistance standards fabricated to utilize the wye-delta transformation, a few challenges present themselves, including the unique quantized resistance in a graphene Hall bar and the limitation of the area of homogeneous high-quality graphene. In this paper, we discuss approaches to optimize the transformation for quantum Hall array resistance standard and propose a dual-output design for 1 M Omega and 100 M Omega as an alternative to other build-up techniques, shortening the path from quantum resistance standards.

By directly integrating a quantum anomalous Hall resistor (QAHR) and a programmable Josephson voltage standard (PJVS) into a single cryostat, we have implemented a unified quantum electrical instrument that provides a realization of the volt, ohm, and ampere in accordance with the revised International System of Units (SI). The quantum voltage output from this prototype ranged from (0.24 to 6.5) mV with combined relative uncertainties (k = 1) down to 3 mu V/V. The colocated QAHR provided a realization of the ohm at zero magnetic field with uncertainties near 1 mu Omega/Omega at R-yx approximate to 25.9 k Omega. For the ampere, a longitudinal current applied to the QAHR is converted to a quantized Hall voltage, which was directly compared to the Josephson voltage, providing measurements of the ampere that are directly traceable to the revised SI. We determined currents in the range (9.33 to 252) nA with uncertainties of (41 to 4.3) mu A/A, respectively. Limitations and improvements are discussed to aid the reproduction of similar instruments at other national metrology institutes.

Advances in the development of graphene-based technology have enabled improvements in DC resistance metrology. Devices made from epitaxially grown graphene have replaced the GaAs-based counterparts, leading to an easier and more accessible realization of the ohm. By optimizing the scale of the growth, it has become possible to fabricate quantized Hall array resistance standards (QHARS) with nominal values between 1 k{\Omega} and 1.29 M{\Omega}. One of these QHARS device designs accommodates a value of about 1.01 M{\Omega}, which made it an ideal candidate to pursue a proof-of-concept that graphene-based QHARS devices are suitable for forming wye-delta resistance networks. In this work, the 1.01 M{\Omega} array output nearly 20.6 M{\Omega} due to the wye-delta transformation, which itself is a special case of star-mesh transformations. These mathematical equivalence principles allow one to extend the QHR to the 100 M{\Omega} and 10 G{\Omega} resistance levels with fewer array elements than would be necessary for a single array with many more elements in series. The 1.01 M{\Omega} device shows promise that the wye-delta transformation can shorten the calibration chain, and, more importantly, provide a chain with a more direct line to the quantum SI.

Photoemission electron microscopy (PEEM) is a unique and powerful tool for studying the electronic properties of materials and surfaces. However, it requires intense and well-controlled light sources with photon energies ranging from the UV to soft X-rays for achieving high spatial resolution and image contrast. Traditionally, many PEEMs were installed at synchrotron light sources to access intense and tunable soft X-rays. More recently, the maturation of solid-state lasers has opened a new avenue for laboratory-based PEEMs using laser-based UV light at lower photon energies. Here, we report on the characteristics of a laser-based UV light source that was recently integrated with a PEEM instrument. The system consists of a high repetition rate, tunable wavelength laser coupled to a harmonics generation module, which generates deep-UV radiation from 192 nm to 210 nm. We comment on the spectral characteristics and overall laser system stability, as well as on the effects of space charge within the PEEM microscope at high UV laser fluxes. Further, we show an example of imaging on gallium nitride, where the higher UV photon energy and flux of the laser provides considerably improved image quality, compared to a conventional light source. These results demonstrate the capabilities of laser-based UV light sources for advancing laboratory-based PEEMs.

We have demonstrated the fabrication of both armchair and zigzag epitaxial graphene nanoribbon (GNR) devices on 4H–SiC using a polymer-assisted sublimation growth method. The phenomenon of terrace step formation has traditionally introduced the risk of GNR deformation along sidewalls, but a polymer-assisted sublimation method helps mitigate this risk. Each type of 50 nm wide GNR is examined electrically and optically (armchair and zigzag), with the latter method being a check on the quality of the GNR devices and the former using alternating current to investigate resistance attenuation from frequencies above 100 Hz. Rates of attenuation are determined for each type of GNR device, revealing subtle suggested differences between armchair and zigzag GNRs.

We present evidence of the direct insulator-quantum Hall transition in monolayer epitaxial graphene, a genuine two-dimensional (2D) system. We studied the transition from an insulating state to a quantum Hall state at a high Landau level filling factor nu = 6 > 3 and the plateau-plateau transition from nu = 6 to nu = 2. Using scaling theory, the critical exponent kappa was determined to be 0.41 +/- 0.02 for the direct insulator-quantum Hall transition. This closely aligns with kappa = 0.42 +/- 0.02 from the nu = 6 to nu = 2 quantum Hall plateau-plateau transition. These findings suggest that the two transitions may belong to the same universality class. While similar transitions have been explored in conventional two-dimensional charge systems, our study provides valuable insights into a truly 2D system, deepening our understanding of these transitions.

We have demonstrated the fabrication of both armchair and zigzag epitaxial graphene nanoribbon (GNR) devices on 4H-SiC using a polymer-assisted sublimation growth method. The phenomenon of terrace step formation has traditionally introduced the risk of GNR deformation along sidewalls, but a polymer-assisted sublimation method helps mitigate this risk. Each type of 50 nm wide GNR is examined electrically and optically (armchair and zigzag), with the latter method being a check on the quality of the GNR devices and the former using alternating current to investigate resistance attenuation from frequencies above 100 Hz. Rates of attenuation are determined for each type of GNR device, revealing subtle suggested differences between armchair and zigzag GNRs.

As the global implementation of new technologies continues to progress, one should hope that a more universal accessibility to the quantum SI is established. This chapter intends to give historical context for the role of the quantum Hall effect in metrology, including a basic overview of the effect, supporting metrology technologies, and how the research in this field has expanded the world's general capabilities. The present-day era of resistance metrology, heavily dominated by the transition from using gallium-arsenide-based devices to graphene-based ones, will be summarized in terms of how the new 2D material performs, how the world has started to implement it as a resistance standard, and how the corresponding measurement infrastructure is currently adapting to the new standard. In the third section, emerging technologies based on graphene will be introduced to give a brief overview of the possible expansion device capabilities. These ideas and research avenues include p-n junction devices, quantum Hall array devices, and experimental components of ac metrology and the quantum ampere. The chapter then concludes by discussing the possible limitations of graphene-based technology for resistance metrology and looks to explore topological insulators as one potential candidate to, at the very least, supplement graphene-based QHR devices for resistance and electrical current metrology.

A mathematical approach is adopted for optimizing the number of total device elements required for obtaining high effective quantized resistances in graphene-based quantum Hall array devices. This work explores an analytical extension to the use of star–mesh transformations such that fractal-like, or recursive, device designs can yield high enough resistances (like 1 EΩ, arguably the highest resistance with meaningful applicability) while still being feasible to build with modern fabrication techniques. Epitaxial graphene elements are tested, whose quantized Hall resistance at the ν=2 plateau (RH≈ 12 906.4 Ω) becomes the building block for larger effective, quantized resistances. It is demonstrated that, mathematically, one would not need more than 200 elements to achieve the highest pertinent resistances.

A mathematical approach is adopted for optimizing the number of total device elements required for obtaining high effective quantized resistances in graphene-based quantum Hall array devices. This work explores an analytical extension to the use of star-mesh transformations such that fractal-like, or recursive, device designs can yield high enough resistances (like 1 E{\Omega}, arguably the highest resistance with meaningful applicability) while still being feasible to build with modern fabrication techniques. Epitaxial graphene elements are tested, whose quantized Hall resistance at the nu=2 plateau (R_H = 12906.4 {\Omega}) becomes the building block for larger effective, quantized resistances. It is demonstrated that, mathematically, one would not need more than 200 elements to achieve the highest pertinent resistances

Advances in the development of graphene-based technology have enabled improvements in dc resistance metrology. Devices made from epitaxially grown graphene (EG) have replaced the GaAs-based counterparts, leading to an easier and more accessible realization of the ohm. By optimizing the scale of the growth, it has become possible to fabricate quantized Hall array resistance standards (QHARS) with nominal values between 1 $\text{k}\Omega $ and 1.29 $\text{M}\Omega $ . One of these QHARS device designs accommodates a value of about 1.01 $\text{M}\Omega $ , which made it an ideal candidate to pursue a proof-of-concept that graphene-based QHARS devices are suitable for forming wye–delta ( $Y$ – $\Delta$ ) resistance networks. In this work, the 1.01- $\text{M}\Omega $ array output is nearly 20.6 $\text{M}\Omega $ due to the $Y$ – $\Delta $ transformation, which itself is a special case of star–mesh transformations. These mathematical equivalence principles allow one to extend the quantized Hall resistance (QHR) to the 100- $\text{M}\Omega $ and 10- $\text{G}\Omega $ resistance levels with fewer array elements than would be necessary for a single array with many more elements in series. The 1.01- $\text{M}\Omega $ device shows promise that the $Y$ – $\Delta $ transformation can shorten the calibration chain, and, more importantly, provide a chain with a more direct line to the quantum international system of units (SI).

An algorithm is introduced for predicting quantized resistances in graphene p-n junction devices that utilize more than a single entry and exit point for electron flow. Depending on the configuration of an arbitrary number of terminals, electrical measurements yield fractional multiples of the typical quantized Hall resistance at the ν=2 plateau R_H ≈ 12906 Ω and take the form: a/bR_H. This theoretical formulation is independent of material, and applications to other material systems that exhibit quantum Hall behaviors are to be expected. Furthermore, this formulation is supported with experimental data from graphene-based devices with multiple source and drain terminals.

This work reports the dynamics of transient hole doping in epitaxial graphene devices by using nitric acid as an adsorbent. The timescales associated with corresponding desorption processes are extracted from the data. The understanding of reversible hole doping without gating is of crucial importance to those fabricating devices with a particular functionality. Measurements of the electrical and optical properties of several devices postexposure were performed with transport temperatures between 300 and 1.5 K. Ambient conditions are applied to nontransport measurements to replicate the most likely laboratory conditions for handling devices using this doping method. The relevant timescales from transport measurements are compared with results from Raman spectroscopy measurements.