Abstract: Taking into account covalent, Coulomb and van der Waals interactions, we construct the dynamical matrix and calculate the phonon dispersion relations for multilayer crystals of hexagonal boron-nitride. Coulomb interactions account for a strong overbending of optical phonons. Applying and extending Born's long-wave theory to the case of multilayer crystals, we calculate the piezoelectric stress constant equation image as a function of the number of layers equation image. In agreement with group theory, we find that equation image for equation image even; for an uneven number equation image of layers we obtain equation image, i.e. the piezoelectric constant decreases as equation image.

Abstract: The lattice dynamics of low-frequency rigid-plane modes in metallic (graphene multilayers, GML) and in insulating (hexagonal boron-nitride multilayers, BNML) layered crystals is investigated. The frequencies of shearing and compression (stretching) modes depend on the layer number N and are presented in the form of fan diagrams. The results for GML and BNML are very similar. In both cases, only the interactions (van der Waals and Coulomb) between nearest-neighbor planes are effective, while the interactions between more distant planes are screened. A comparison with recent Raman scattering results on low-frequency shear modes in GML [Tan et al., Nat. Mater., in press, doi: 10.1038/nmat3245, (2012)] is made. Relations with the low-lying rigid-plane phonon dispersions in the bulk materials are established. Master curves, which connect the fan diagram frequencies for any given N, are derived. Static and dynamic thermal correlation functions for rigid-layer shear and compression modes are calculated. The results might be of use for the interpretation of friction force experiments on multilayer crystals.

Abstract: We investigate the optimal orientations and positions of tubular fullerene molecules C-70, C-80 and C-90 encapsulated in single-walled carbon nanotubes (SWCNTs). We find that increasing the tube radius leads to the following succession of energetically stable regimes: 1) lying molecules positioned on the tube's long axis, 2) tilted molecules on the tube's long axis and 3) lying molecules shifted away from the tube's long axis. In the case of C-70 and C-80 molecules, standing on-axis configurations also occur. Our findings are relevant for the possible application of molecular-orientation-dependent electronic properties of fullerene nanopeapods.

Abstract: The determination of the layer number ${\cal N}$ in nanoscale thin layered crystals is a challenging problem of technological relevance. In addition to innovative experimental techniques, a thorough knowledge of the underlying lattice dynamics is required. Starting from phenomenological atomic interaction potentials we have carried out an analytical study of the low-frequency optical phonon dispersions in layered crystals. At the gamma point of the two-dimensional Brillouin zone the optical phonon frequencies correspond to rigid-plane shearing and compression modes. We have investigated graphene multilayers (GML) and hexagonal boron-nitride multilayers (BNML). The frequencies show a characteristic dependence on ${\cal N}$. The results which are represented in the form of fan diagrams are very similar for both materials. Due to charge neutrality within layers Coulomb forces play no role, only van der Waals forces between nearest neighbor layers are relevant. The theoretical results agree with recent low-frequency Raman results on rigid-layer modes [Tan et al., Nature Mater. 11, 294 (2012)] in GML and double-resonant Raman scattering data on rigid-layer compression modes [Herziger et al., Phys. Rev. B 85, 235447 (2012)] in GML. (C) 2012 WILEY-VCH Verlag GmbH Co. KGaA, Weinheim

Abstract: The appearance of massless Dirac fermions in graphene requires two equivalent carbon sublattices of trigonal shape. While the generation of an effective mass and a band gap at the Dirac point remains an unresolved problem for freestanding extended graphene, it is well established by breaking translational symmetry by confinement and by breaking sublattice symmetry by interaction with a substrate. One of the strongest sublattice-symmetry-breaking interactions with predicted and measured band gaps ranging from 400 meV to more than 3 eV has been attributed to the interfaces of graphene with Ni and Co, which are also promising spin-filter interfaces. Here, we apply angle-resolved photoemission to epitaxial graphene on Ni (111) and Co(0001) to show the presence of intact Dirac cones 2.8 eV below the Fermi level. Our results challenge the common belief that the breaking of sublattice symmetry by a substrate and the opening of the band gap at the Dirac energy are in a straightforward relation. A simple effective model of a biased bilayer structure composed of graphene and a sublattice-symmetry-broken layer, corroborated by density-functional-theory calculations, demonstrates the general validity of our conclusions.