  We report on the configurations and electronic properties of graphyne and
graphdiyne nanoribbons with armchair and zigzag edges investigated with first
principles calculations. Our results show that all the nanoribbons are
semiconductors with suitable band gaps similar to silicon. And their band gaps
decrease as widths of nanoribbons increase. We also find that the band gap is
at the Gamma point for all graphdiyne ribbons and it is at the X point for all
graphyne ribbons. Of particular interest, the band gap of zigzag graphyne
nanoribbons show a unique step effect as the width increases. This property is
good for tuning of the energy band gap, as in a certain range of the ribbon
width, the energy gap remains constant and in reality the edge cannot be as
neat as that in a theoretic model.
