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. 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. Of particular interest might be the properties of topological defects between the two commensurate phases: solitons, domain walls, and dislocation walls. Here we report a commensurate-incommensurate transition for graphene on top of hexagonal boron nitride (hBN). 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, and their presence might explain recent observations when the electronic, optical, Raman and other properties of graphene-hBN heterostructures have been notably altered.
Graphene is one of the stiffest known materials, with a Youngs modulus of 1 TPa, making it an ideal candidate for use as a reinforcement in high-performance composites. However, being a one-atom thick crystalline material, graphene poses several fund
amental questions: (1) can decades of research on carbon-based composites be applied to such an ultimately-thin crystalline material? (2) is continuum mechanics used traditionally with composites still valid at the atomic level? (3) how does the matrix interact with the graphene crystals and what kind of theoretical description is appropriate? We have demonstrated unambiguously that stress transfer takes place from the polymer matrix to monolayer graphene, showing that the graphene acts as a reinforcing phase. We have also modeled the behavior using shear-lag theory, showing that graphene monolayer nanocomposites can be analyzed using continuum mechanics. Additionally, we have been able to monitor stress transfer efficiency and breakdown of the graphene/polymer interface.
Graphene is only one atom thick, optically transparent, chemically inert and an excellent conductor. These properties seem to make this material an excellent candidate for applications in various photonic devices that require conducting but transpare
nt thin films. In this letter we demonstrate liquid crystal devices with electrodes made of graphene which show excellent performance with a high contrast ratio. We also discuss the advantages of graphene compared to conventionally-used metal oxides in terms of low resistivity, high transparency and chemical stability.
