Graphitic ribbons without hydrogen-termination: Electronic structures and stabilities

The graphitic ribbons with H termination have been the subject of recent studies, but we investigated the ribbons without H termination using tight-binding and first-principles calculations. The ribbons with armchair edge were found to have phonon frequencies near 2000 cm^-1 which has been solely ascribed to the one-dimensional carbon allotrope, carbyne. Comparative studies of the formation energies suggest that ribbons will grow more easily in the direction perpendicular to the zigzag edge, consistent with a recent experiment.