Low-Energy Electronic Properties of Graphene and Armchair Ribbon Superlattices

The geometric structures and electronic properties of graphene and armchair ribbon superlattices are investigated by the first-principles calculations. Parallel armchair ribbons are periodically placed upon a graphene sheet. The interlayer atomic interactions strongly influence the interlayer distance, binding energy, energy dispersion, state degeneracy, band gap, Fermi velocity, and Fermi momentum except for the intralayer bond length. These properties depend on the stacking configurations, ribbon width, and existence of hydrogen atoms at the ribbon edges. Such interactions also result in the distortion of graphene and ribbons, which is more obvious in the AA-stacked systems than the AB-stacked ones. All low-energy bands come from the 2p(z) orbitals of graphene or ribbon or from those of both. Most AA-stacked systems possess two intersecting low-lying bands, which exhibit highly anisotropic Fermi velocities. AB-stacked systems mainly have a direct band gap that is monotonously widened as ribbon width expands.