The quantum Hall effect allows the international standard for resistance to be defined in terms of the electron charge and Planck's constant alone. The effect comprises the quantization of the Hall resistance in two-dimensional electron systems in rational fractions of R(K) = h/e(2) = 25,812.807557(18) Omega, the resistance quantum. Despite 30 years of research into the quantum Hall effect, the level of precision necessary for metrology--a few parts per billion--has been achieved only in silicon and iii-v heterostructure devices. Graphene should, in principle, be an ideal material for a quantum resistance standard, because it is inherently two-dimensional and its discrete electron energy levels in a magnetic field (the Landau levels) are widely spaced. However, the precisions demonstrated so far have been lower than one part per million. Here, we report a quantum Hall resistance quantization accuracy of three parts per billion in monolayer epitaxial graphene at 300 mK, four orders of magnitude better than previously reported. Moreover, by demonstrating the structural integrity and uniformity of graphene over hundreds of micrometres, as well as reproducible mobility and carrier concentrations across a half-centimetre wafer, these results boost the prospects of using epitaxial graphene in applications beyond quantum metrology.

We compare the three most commonly used scanning probe techniques to obtain a reliable value of the work function in graphene domains of different thickness. The surface potential (SP) of graphene is directly measured in Hall bar geometry via a combination of electrical functional microscopy and spectroscopy techniques, which enables calibrated work function measurements of graphene domains in ambient conditions with values Φ1LG ~4.55 ± 0.02 eV and Φ2LG ~ 4.44 ± 0.02 eV for single- and bi-layer, respectively. We demonstrate that frequency-modulated Kelvin probe force microscopy (FM-KPFM) provides more accurate measurement of the SP than amplitude-modulated (AM)-KPFM. The discrepancy between experimental results obtained by different techniques is discussed. In addition, we use FM-KPFM for contactless measurements of the specific components of the device resistance. We show a strong non-Ohmic behavior of the electrode-graphene contact resistance and extract the graphene channel resistivity.

Twisted heterostructures of two-dimensional crystals offer almost unlimited scope for the design of new metamaterials. Here we demonstrate a room temperature ferroelectric semiconductor that is assembled using mono- or few-layer MoS2. These van der Waals heterostructures feature broken inversion symmetry, which, together with the asymmetry of atomic arrangement at the interface of two 2D crystals, enables ferroelectric domains with alternating out-of-plane polarization arranged into a twist-controlled network. The last can be moved by applying out-of-plane electrical fields, as visualized in situ using channelling contrast electron microscopy. The observed interfacial charge transfer, movement of domain walls and their bending rigidity agree well with theoretical calculations. Furthermore, we demonstrate proof-of-principle field-effect transistors, where the channel resistance exhibits a pronounced hysteresis governed by pinning of ferroelectric domain walls. Our results show a potential avenue towards room temperature electronic and optoelectronic semiconductor devices with built-in ferroelectric memory functions.

The sensitivity of graphene to the surrounding environment is given by its π electrons, which are directly exposed to molecules in the ambient. The high sensitivity of graphene to the local environment has shown to be both advantageous but also problematic for graphene-based devices, such as transistors and sensors, where the graphene carrier concentration and mobility change due to ambient humidity variations. In this review, recent progress in understanding the effects of water on different types of graphene, grown epitaxially and quasi-free standing on SiC, by chemical vapour deposition on SiO2, as well as exfoliated flakes, are presented. It is demonstrated that water withdraws electrons from graphene, but the graphene-water interaction highly depends on the thickness, layer stacking, underlying substrate and substrate-induced doping. Moreover, we highlight the importance of clear and unambiguous description of the environmental conditions (i.e. relative humidity) whenever a routine characterisation for carrier concentration and mobility is reported (often presented as a simple figure-of-merit), as these electrical characteristics are highly dependent on the adsorbed molecules and the surrounding environment.

This article addresses the much debated question whether the degree of hydrophobicity of single-layer graphene (1LG) is different from that of double-layer graphene (2LG). Knowledge of the water affinity of graphene and its spatial variations is critically important as it can affect the graphene properties as well as the performance of graphene devices exposed to humidity. By employing chemical force microscopy with a probe rendered hydrophobic by functionalization with octadecyltrichlorosilane (OTS), the adhesion force between the probe and epitaxial graphene on SiC has been measured in deionized water. Owing to the hydrophobic attraction, a larger adhesion force was measured on 2LG Bernal-stacked domains of graphene surfaces, thus showing that 2LG is more hydrophobic than 1LG. Identification of 1LG and 2LG domains was achieved through Kelvin probe force microscopy and Raman spectral mapping. Approximate values of the adhesion force per OTS molecule have been calculated through contact area analysis. Furthermore, the contrast of friction force images measured in contact mode was reversed to the 1LG/2LG adhesion contrast, and its origin was discussed in terms of the likely water depletion over hydrophobic domains as well as deformation in the contact area between the atomic force microscope tip and 1LG.

Since it was first demonstrated in 1987, magnetic force microscopy (MFM) has become a truly widespread and commonly used characterization technique that has been applied to a variety of research and industrial applications. Some of the main advantages of the method includes its high spatial resolution (typically ∼50 nm), ability to work in variable temperature and applied magnetic fields, versatility, and simplicity in operation, all without almost any need for sample preparation. However, for most commercial systems, the technique has historically provided only qualitative information, and the number of available modes was typically limited, thus not reflecting the experimental demands. Additionally, the range of samples under study was largely restricted to “classic” ferromagnetic samples (typically, thin films or patterned nanostructures). Throughout this Perspective article, the recent progress and development of MFM is described, followed by a summary of the current state-of-the-art techniques and objects for study. Finally, the future of this fascinating field is discussed in the context of emerging instrumental and material developments. Aspects including quantitative MFM, the accurate interpretation of the MFM images, new instrumentation, probe-engineering alternatives, and applications of MFM to new (often interdisciplinary) areas of the materials science, physics, and biology will be discussed. We first describe the physical principles of MFM, specifically paying attention to common artifacts frequently occurring in MFM measurements; then, we present a comprehensive review of the recent developments in the MFM modes, instrumentation, and the main application areas; finally, the importance of the technique is speculated upon for emerging or anticipated to emerge fields including skyrmions, 2D-materials, and topological insulators.

Abstract:We present local electrical characterization of epitaxial graphene grown on both Si-and C-faces of 4H-SiC using Electrostatic Force Microscopy and Kelvin Probe Force Microscopy in ambient conditions and at elevated temperatures. These techniques provide a straightforward identification of graphene domains with various thicknesses on the substrate where topographical determination is hindered by adsorbates and SiC terraces. We also use Electrostatic Force Spectroscopy which allows quantitative surface potential measurements with high spatial resolution. Using these techniques, we study evolution of a layer of atmospheric water as a function of temperature, which is accompanied by a significant change of the absolute surface potential difference. We show that the nanoscale wettability of the material is strongly dependent on the number of graphene layers, where hydrophobicity increases with graphene thickness. We also use micron-sized graphene Hall bars with gold electrodes to calibrate work function of the electrically conductive probe and precisely and quantitatively define the work functions for single-and double-layer graphene.

Two-dimensional (2D) semiconductors -atomic layers of materials with covalent intra-layer bonding and weak (van der Waals or quadrupole) coupling between the layers 1are a new class of materials with great potential for optoelectronic applications 2 . Among those, a special position is now being taken by post-transition metal chalcogenides (PTMC), InSe and GaSe. It has recently been found 3 that the band gap in 2D crystals of InSe more than doubles in the monolayer compared to thick multilayer crystals, while the high mobility of conduction band electrons is promoted by their light in-plane mass. Here, we use Raman and PL measurements of encapsulated few layer samples, coupled with accurate atomic force and transmission electron microscope structural characterisation to reveal new optical properties of atomically thin GaSe preserved by hBN encapsulation. The band gaps we observe complement the spectral range provided by InSe films, so that optical activity of these two almost latticematched PTMC films and their heterostructures densely cover the spectrum of photons from violet to infrared. We demonstrate the realisation of the latter by the first observation of interlayer excitonic photoluminescence in few-layer InSe/GaSe heterostructures. The spatially indirect transition is direct in k-space and therefore is bright, while its energy can be tuned in a broad range by the number of layers.