Low-energy electronic structures of nanotube-graphene hybrid carbon systems

Electronic structures of nanotube-graphene hybrid carbon systems are calculated by the tight-binding model. The Lennard-Jones potential is used to determine the optimal geometry between nanotubes and a monolayer graphene. The periodic alignment of nanotubes on graphene results in quasi-one-dimensional physical phenomena. The low-frequency energy dispersions are significantly influenced by the interlayer interactions, such as the removal of subband degeneracy, creation of extra band-edge states, and modulation of energy gaps. The composite systems could be either metals or semiconductors according to the alignment and geometry of nanotubes.