Band gap oscillation and novel transport property in ultrathin chiral graphene nanoribbons

We report a numerical study of the edge states in chiral graphene nanoribbons (cGNRs) within the tight-binding approximation. For ultrathin ribbons, band gap oscillations are found as a function of the ribbon width, with a period of 3a, where a is the lattice constant of cGNRs. With the increasing ribbon width, the oscillation is found to be dampened at a critical width, depending on the chiral angle of the cGNRs. In addition, the chiral angle and the width of the cGNR also influence the generation of the edge states. Through the transfer matrix technique, we demonstrate that the energy dependence of the conductance exhibits an unusual step-like feature for cGNRs.