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Hexagonal lattice
About: Hexagonal lattice is a research topic. Over the lifetime, 7875 publications have been published within this topic receiving 153922 citations.
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TL;DR: This work illustrates the concept of graphene as a robust atomic-scale scaffold on the basis of which new two-dimensional crystals with designed electronic and other properties can be created by attaching other atoms and molecules.
Abstract: Although graphite is known as one of the most chemically inert materials, we have found that graphene, a single atomic plane of graphite, can react with atomic hydrogen, which transforms this highly conductive zero-overlap semimetal into an insulator. Transmission electron microscopy reveals that the obtained graphene derivative (graphane) is crystalline and retains the hexagonal lattice, but its period becomes markedly shorter than that of graphene. The reaction with hydrogen is reversible, so that the original metallic state, the lattice spacing, and even the quantum Hall effect can be restored by annealing. Our work illustrates the concept of graphene as a robust atomic-scale scaffold on the basis of which new two-dimensional crystals with designed electronic and other properties can be created by attaching other atoms and molecules.
3,735 citations
TL;DR: In this paper, the results of scanning tunnelling microscopy and spectroscopy on individual single-walled nanotubes from which atomically resolved images allow us to examine electronic properties as afunction of tube diameter and wrapping angle.
Abstract: Carbon nanotubes can be thought of as graphitic sheets with a hexagonal lattice that have been wrapped up into a seamless cylinder. Since their discovery in 19911, the peculiar electronic properties of these structures have attracted much attention. Their electronic conductivity, for example, has been predicted2,3,4 to depend sensitively on tube diameter and wrapping angle (a measure of the helicity of the tube lattice), with only slight differences in these parameters causing a shift from a metallic to a semiconducting state. In other words, similarly shaped molecules consisting of only one element (carbon) may have very different electronic behaviour. Although the electronic properties of multi-walled and single-walled nanotubes5,6,7,8,9,10,11,12 have been probed experimentally, it has not yet been possible to relate these observations to the corresponding structure. Here we present the results of scanning tunnelling microscopy and spectroscopy on individual single-walled nanotubes from which atomically resolved images allow us to examine electronic properties as afunction of tube diameter and wrapping angle. We observe bothmetallic and semiconducting carbon nanotubes and find thatthe electronic properties indeed depend sensitively on thewrapping angle. The bandgaps of both tube types are consistent with theoretical predictions. We also observe van Hove singularities at the onset of one-dimensional energy bands, confirming the strongly one-dimensional nature of conduction within nanotubes.
2,797 citations
TL;DR: For all cubic lattices the method of Monkhorst and Pack generates not only point sets identical to those obtained by Chadi and Cohen, but also intermediate sets with the same properties as mentioned in this paper.
Abstract: It is again emphasized that for all cubic lattices the method of Monkhorst and Pack generates not only point sets identical to those obtained by Chadi and Cohen, but also intermediate sets with the same properties. In addition, a comparison of these two methods for the hexagonal lattice reveals our method to be more flexible and efficient.
2,310 citations
TL;DR: Atomic structures and nanoscale morphology of graphene-based electronic devices are revealed for the first time and a strong spatially dependent perturbation is revealed which breaks the hexagonal lattice symmetry of the graphitic lattice.
Abstract: We employ scanning probe microscopy to reveal atomic structures and nanoscale morphology of graphene-based electronic devices (i.e., a graphene sheet supported by an insulating silicon dioxide substrate) for the first time. Atomic resolution scanning tunneling microscopy images reveal the presence of a strong spatially dependent perturbation, which breaks the hexagonal lattice symmetry of the graphitic lattice. Structural corrugations of the graphene sheet partially conform to the underlying silicon oxide substrate. These effects are obscured or modified on graphene devices processed with normal lithographic methods, as they are covered with a layer of photoresist residue. We enable our experiments by a novel cleaning process to produce atomically clean graphene sheets.
1,497 citations
TL;DR: In this paper, the dipole-dipolecular repulsive interactions organize polystyrene spheres into a two-dimensional triangular lattice and direct microscopic observations of such an interfacial colloidal crystal are reported for the first time.
Abstract: Polystyrene spheres (2450 \AA{} in diameter) are trapped in a surface energy well at water/air interface. Because of asymmetry of charge distribution, electrical dipoles are associated with each interfacial particle. The dipole-dipole repulsive interactions organize the polystyrene spheres into a two-dimensional triangular lattice. The direct microscopic observations of such an interfacial colloidal crystal are reported for the first time.
1,235 citations