Two-dimensional (2D) materials such as graphene have become the focus of extensive research efforts in condensed matter physics. They provide opportunities for both fundamental research and applications across a wide range of industries. Ideally, characterization of graphene requires non-invasive techniques with single-atomic-layer thickness resolution and nanometer lateral resolution. Moreover, commercial application of graphene requires fast and large-area scanning capability. We demonstrate the optimized balance of image resolution and acquisition time of non-invasive confocal laser scanning microscopy (CLSM), rendering it an indispensable tool for rapid analysis of mass-produced graphene. It is powerful for analysis of 1–5 layers of exfoliated graphene on Si/SiO₂, and allows us to distinguish the interfacial layer and 1–3 layers of epitaxial graphene on SiC substrates. Furthermore, CLSM shows excellent correlation with conventional optical microscopy, atomic force microscopy, Kelvin probe force microscopy, conductive atomic force microscopy, scanning electron microscopy and Raman mapping.

In this paper, we show that quantum Hall resistance measurements using two terminals may be as precise as four-terminal measurements when applying superconducting split contacts. The described sample designs eliminate resistance contributions of terminals and contacts such that the size and complexity of next-generation quantized Hall resistance devices can be significantly improved.

The quantum Hall effect (QHE), and devices reliant on it, will continue to serve as the foundation of the ohm while also expanding its territory into other SI derived units. The foundation, evolution, and significance of all of these devices exhibiting some form of the QHE will be described in the context of optimizing future electrical resistance standards. As the world adapts to using the quantum SI, it remains essential that the global metrology community pushes forth and continues to innovate and produce new technologies for disseminating the ohm and other electrical units.

We report the performance of a quantum Hall resistance standard based on epitaxial graphene maintained in a 5-T tabletop cryocooler system. This quantum resistance standard requires no liquid helium and can operate continuously, allowing year-round accessibility to quantized Hall resistance measurements. The ν = 2 plateau, with a value of R _K /2, also seen as R _H , is used to scale to 1 kQ using a binary cryogenic current comparator (BCCC) bridge and a direct current comparator (DCC) bridge. The uncertainties achieved with the BCCC are such as those obtained in the state-of-the-art measurements using GaAs-based devices. BCCC scaling methods can achieve large resistance ratios of 100 or more, and while room temperature DCC bridges have smaller ratios and lower current sensitivity, they can still provide alternate resistance scaling paths without the need for cryogens and superconducting electronics. Estimates of the relative uncertainties of the possible scaling methods are provided in this report, along with a discussion of the advantages of several scaling paths. The tabletop system limits are addressed as are potential solutions for using graphene standards at higher currents.