When a crystal is subjected to a periodic potential, under certain circumstances (such as when the period of the potential is close to the crystal periodicity; the potential is strong enough, etc.) it might adjust itself to follow the periodicity of the potential, resulting in a, so called, commensurate state 1-3 .Such commensurate-incommensurate transitions are ubiquitous phenomena in many areas of condensed matter physics: from magnetism and dislocations in crystals, to vortices in superconductors, and atomic layers adsorbed on a crystalline surface 1 . Of particular interest might be the properties of topological defects between the two commensurate phases: solitons 2,4 , domain walls 1 , and dislocation walls 5-7 . Here we report a commensurate-incommensurate transition for graphene on top of hexagonal boron nitride (hBN) 8,9 . Depending on the rotational angle between the two hexagonal lattices, graphene can either stretch to adjust to a slightly different hBN periodicity (the commensurate state found for small rotational angles) or exhibit little adjustment (the incommensurate state). In the commensurate state, areas with matching lattice constants are separated by domain walls that accumulate the resulting strain. Such soliton-like objects present significant fundamental interest 1 , and their presence might explain recent observations when the electronic, optical, Raman and other properties of graphene-hBN heterostructures have been notably altered 10 .

Recent developments in the technology of van der Waals heterostructures made from two-dimensional atomic crystals have already led to the observation of new physical phenomena, such as the metal-insulator transition and Coulomb drag, and to the realization of functional devices, such as tunnel diodes, tunnel transistors and photovoltaic sensors. An unprecedented degree of control of the electronic properties is available not only by means of the selection of materials in the stack, but also through the additional fine-tuning achievable by adjusting the built-in strain and relative orientation of the component layers. Here we demonstrate how careful alignment of the crystallographic orientation of two graphene electrodes separated by a layer of hexagonal boron nitride in a transistor device can achieve resonant tunnelling with conservation of electron energy, momentum and, potentially, chirality. We show how the resonance peak and negative differential conductance in the device characteristics induce a tunable radiofrequency oscillatory current that has potential for future high-frequency technology.

Summary• White lupin (Lupinus albus) forms specialized cluster roots characterized by exudation of organic anions under phosphorus (P) deficiency. Here, the role of nitric oxide (NO) in P deficiency-induced cluster-root formation and citrate exudation was evaluated.• White lupin plants were treated with the NO donor sodium nitroprusside (SNP) and scavenger or inhibitor of NO synthase under conditions of P deficiency (0 lM) or P sufficiency (50 lM).• Phosphorus deficiency enhanced NO production in primary and lateral root tips, with a greater increase in cluster roots than in noncluster roots. NO concentrations decreased with cluster root development from the pre-emergent stage, through the juvenile stage, to the mature stage. The P deficiency-induced increase in NO production was inhibited by antagonists of NO synthase and xanthine oxidoreductase, suggesting the involvement of these enzymes in NO production. SNP markedly increased the number of cluster roots. Citrate exudation from different root segments in P-deficient roots was positively correlated with endogenous root NO concentrations.• These findings demonstrate differential patterns of NO production in white lupin, depending on root zone, developmental stage and P nutritional status. NO appears to play a regulatory role in the formation of cluster roots and citrate exudation in white lupin under conditions of P deficiency.

Exploring how hydrophilicity regulates catalytic properties at the molecular level remains a grand challenge, although it has great potential to offer guidelines for developing highly efficient catalysts and deepen the mechanistic understanding of heterogeneous catalysis. Here, we provide molecular-level insight into the influence of surface hydroxyl groups on hydrophilic SiC quantum dots (QDs) on CO 2 hydrogenation. In CO 2 hydrogenation into methanol, SiC QDs exhibited higher catalytic activity and lower activation energy than commercial SiC. Mechanistic studies revealed that the surface hydroxyl species on SiC QDs was directly involved in CO 2 hydrogenation through the addition of H atoms in hydroxyl groups into CO 2 to form HCOO* as the intermediate. The unique reaction path decreased the energy barrier for the formation of HCOO*, facilitating the activation of CO 2 . Our understanding of surface hydrophilicity directly instructs the development of efficient catalysts toward CO 2 hydrogenation.