Within a tight-binding approach we investigate how the electronic structure evolves from a single graphene layer into bulk graphite by computing the band structure of one, two, and three layers of graphene. It is well known that a single graphene layer is a zero-gap semiconductor with a linear Dirac-like spectrum around the Fermi energy, while graphite shows a semimetallic behavior with a band overlap of about 41 meV. In contrast to a single graphene layer, we show that two graphene layers have a parabolic spectrum around the Fermi energy and are a semimetal like graphite; however, the band overlap of 0.16 meV is extremely small. Three and more graphene layers show a clear semimetallic behavior. For 11 and more layers the difference in band overlap with graphite is smaller than 10%.

Different stoichiometric configurations of graphane and graphene fluoride are investigated within density functional theory. Their structural and electronic properties are compared, and we indicate the similarities and differences among the various configurations. Large differences between graphane and graphene fluoride are found that are caused by the presence of charges on the fluorine atoms. A new configuration that is more stable than the boat configuration is predicted for graphene fluoride. We also perform GW calculations for the electronic band gap of both graphene derivatives. These band gaps and also the calculated Young's moduli are at variance with available experimental data. This might indicate that the experimental samples contain a large number of defects or are only partially covered with H or F.Comment: 6 pages, 3 figures, submitted to PR

We have performed a first-principles density functional theory investigation of the penetration of helium atoms through a graphene monolayer with defects. The relaxation of the graphene layer caused by the incoming helium atoms does not have a strong influence on the height of the energy barriers for penetration. For defective graphene layers, the penetration barriers decrease exponentially with the size of the defects but they are still sufficiently high that very large defects are needed to make the graphene sheet permeable for small atoms and molecules. This makes graphene a very promising material for the construction of nanocages and nanomembranes.Graphene is one of the most studied materials these days, which has resulted already in a large amount of proposals for possible applications. 1 These applications range from very sensitive gas sensors 2 to carbon-based electronics 3 and are mainly based on the essentially twodimensional (2D) form of graphene and the Dirac-like behavior of the electrons at the Fermi level. 4 Recently it was experimentally shown that perfect graphene sheets are impermeable to standard gases, including helium. 5 This introduces a new range of applications for graphene as an ultrathin, but still impermeable, membrane. In Ref. 5, Bunch et al. suggested also that the graphene samples should be free of defects to explain the impermeability. This suggestion was based on a simple classical effusion theory calculation of the penetration of point particles through single atom vacancies in graphene. In this letter, however, we demonstrate through ab initio calculations that defective graphene is still impermeable and that large defects are needed to destroy this impermeability. In our study we concentrate on the penetration of helium atoms through graphene with increasingly large defects. Helium atoms are the smallest atoms that do not chemically interact with graphene. We limit ourselves to point defects that keep the sp 2 hybridization of the carbon atoms of graphene more or less intact. Such defects are more stable 6,7 and easier to treat in first-principles calculations.We make use of the density functional theory (DFT) formalism in both the local density (LDA) and general gradient approximation (GGA). All our DFT calculations are performed with the ABINIT 8 software package. The simulation of most defects is done in a 4 × 4 × 4 graphene supercell with a distance of 16Å between adjacent graphene layers. A plane-wave basis with a cutoff energy of 30 Hartree (816 eV) was used and the Brioullin zone (BZ) is sampled with a 6 × 6 × 6 Monckhorst-Pack (MP) 9 k-point grid which is equivalent to a 24 × 24 × 24 MP grid in a single unit cell. We used pseudopotentials of the Troullier-Martins type 10 for both the LDA and GGA calculations. There is no need to perform spinpolarized calculations because the defects were chosen to preserve the sp 2 hybridization of the carbon atoms in the simulated defective graphene sheets and the He atom is inert.We first examine the penetration of a helium atom throug...

We apply density-functional theory to study the adsorption of water clusters on the surface of a graphene sheet and find i͒ graphene is highly hydrophobic and ii͒ adsorbed water has very little effect on the electronic structure of graphene. A single water cluster on graphene has a very small average dipole moment which is in contrast with an ice layer that exhibits a strong dipole moment.