In the quantum anomalous Hall effect, quantized Hall resistance and vanishing longitudinal resistivity are predicted to result from the presence of dissipationless, chiral edge states and an insulating two-dimensional bulk, without requiring an external magnetic field. Here, we explore the potential of this effect in magnetic topological insulator thin films for metrological applications. Using a cryogenic current comparator system, we measure quantization of the Hall resistance to within one part per million and, at lower current bias, longitudinal resistivity under 10 mΩ at zero magnetic field. Increasing the current density past a critical value leads to a breakdown of the quantized, low-dissipation state, which we attribute to electron heating in bulk current flow. We further investigate the prebreakdown regime by measuring transport dependence on temperature, current, and geometry, and find evidence for bulk dissipation, including thermal activation and possible variable-range hopping.

The transport characteristics of graphene devices with low n‐ or p‐type carrier density (∼1010–1011 cm‐2), fabricated using a new process that results in minimal organic surface residues, are reported. The p‐type molecular doping responsible for the low carrier densities is initiated by aqua regia. The resulting devices exhibit highly developed ν = 2 quantized Hall resistance plateaus at magnetic field strengths of less than 4 T.

Quantized magnetotransport is observed in 5.6 × 5.6 mm2 epitaxial graphene devices, grown using highly constrained sublimation on the Si-face of SiC(0001) at high temperature (1900 °C). The precise quantized Hall resistance of Rxy=h2e2 is maintained up to record level of critical current Ixx = 0.72 mA at T = 3.1 K and 9 T in a device where Raman microscopy reveals low and homogeneous strain. Adsorption-induced molecular doping in a second device reduced the carrier concentration close to the Dirac point (n ≈ 1010 cm−2), where mobility of 18760 cm2/V is measured over an area of 10 mm2. Atomic force, confocal optical, and Raman microscopies are used to characterize the large-scale devices, and reveal improved SiC terrace topography and the structure of the graphene layer. Our results show that the structural uniformity of epitaxial graphene produced by face-to-graphite processing contributes to millimeter-scale transport homogeneity, and will prove useful for scientific and commercial applications.

This paper describes a recent determination of the von Klitzing constant and the fine-structure constant by comparisons of values of the ohm as defined in the International System of Units (SI), derived from the National Institute of Standards and Technology (NIST) calculable cross-capacitor, and values of the international practical unit of resistance derived from the integral quantum Hall effect. In this determination, the comparisons were made in a series of measurements lasting three years. A small difference is observed between this determination and an earlier comparison carried out in this laboratory and reported in 1988. The most recent value of the fine-structure constant based on the experimental value and theoretical expression for the magnetic moment anomaly of the electron, which has the smallest uncertainty of any value currently available, is consistent with both of these results. The new value exceeds the 1990 conventional value of the von Klitzing constant by slightly more than twice the relative standard uncertainty of the present measurement, which is 2.4 10 -8 .

Graphene-based quantised Hall resistance standards promise high precision for the unit ohm under less exclusive measurement conditions, enabling the use of compact measurement systems. To meet the requirements of metrological applications, national metrology institutes developed large-area monolayer graphene growth methods for uniform material properties and optimized device fabrication techniques. Precision measurements of the quantized Hall resistance showing the advantage of graphene over GaAs-based resistance standards demonstrate the remarkable achievements realized by the research community. This work provides an overview over the state-of-the-art technologies in this field.

Abstract-The latest NIST result from the comparison of the quantized Hall resistance (QHR) with the realization of the SI ohm obtained from the NIST calculable capacitor is reported. A small difference between the 1988 result and the present result has led to a re-evaluation of the sources and magnitudes of possible systematic errors.

Confocal laser scanning microscopy (CLSM) is a non-destructive, highly-efficient optical characterization method for large-area analysis of graphene on different substrates, which can be applied in ambient air, does not require additional sample preparation, and is insusceptible to surface charging and surface contamination. CLSM leverages optical properties of graphene and provides greatly enhanced optical contrast and mapping of thickness down to a single layer.We demonstrate the effectiveness of CLSM by measuring mechanically exfoliated and chemical vapor deposition graphene on Si/SiO2, and epitaxial graphene on SiC. In the case of graphene on Si/SiO2, both CLSM intensity and height mapping is powerful for analysis of 1-5 layers of graphene. For epitaxial graphene on SiC substrates, the CLSM intensity allows us to distinguish features such as dense, parallel 150 nm wide ribbons of graphene (associated with the early stages of the growth process) and large regions covered by the interfacial layer and 1-3 layers of graphene.In both cases, CLSM data shows excellent correlation with conventional optical microscopy, atomic force microscopy, Kelvin probe force microscopy, conductive atomic force microscopy, influence on the layer growth and uniformity 5,32 . Recently, KPFM was shown to be a more reliable method for distinguishing the number of EG layers 33 . Nonetheless, Raman and SPM methods are time consuming and typically limit the scan size to a few tens of micrometers. Scaling up the production process requires fast and accurate characterization of the material quality at the wafer scale, while at the same time retaining sub-micrometer spatial resolution.In this report, we demonstrate that reflection mode CLSM is a superior tool for rapid characterization of large-area graphene and graphene nanostructures on Si/SiO2 and SiC, compared to conventional optical microscopy (OM), Raman spectroscopy, AFM, conductive atomic force microscopy (C-AFM), KPFM, and scanning electron microscope (SEM) methods.CLSM can simultaneously produce intensity and topography images as well as has a lateral resolution that can be pushed beyond the optical diffraction limit. The depth-of-field is enhanced by digitally selecting in-focus regions from multiple images at different focal planes, enabling high resolution over larger areas. First, we discuss CLSM results on various thicknesses of exfoliated graphene transferred to Si/SiO2 substrate. By comparing the results to AFM and Raman measurements, we present a method for assessing the CLSM intensity and height for graphene of different thicknesses. Next, we apply CLSM and Raman spectroscopy to CVD-grown graphene transferred to Si/SiO2 substrate to demonstrate fast and accurate, large-scale analysis. Finally, we apply CLSM to epitaxial graphene on SiC demonstrating the speed, accuracy, and versatility of CLSM compared to OM, SEM, AFM, KPFM, C-AFM and Raman microscopy. RESULTS Exfoliated graphene on Si/SiO2

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.