▎ 摘　　要

A new family of planar nanostructures having graphene-like electronic band structure is theoretically investigated by density functional theory (DFT). Based on general perturbation theory and a tight-binding model, it was shown that graphene-like planar structures, consisting of identical nanoparticles with relatively weak contacts between them, should have an electronic band structure with Dirac cones. Two such structures, consisting of 71- or 114-silicon atom nanoparticles, were investigated by DFT using VASP software package. The band-structure calculations show the presence of Dirac cones with electron group velocity equal to 1.05 x 10(5) and 0.53 x 10(5) m/s, respectively. By generalizing the theory, a new family of 3D structures having intersecting areas with linear dispersion in the band structures was derived. As an example, the band structure of identical 25-atom silicon nanoclusters arranged in a simple cubic lattice was calculated. It was shown that the band structure has features similar to the Dirac cones. (C) 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim