▎ 摘　　要

Narrow graphene nanoribbons are a promising channel material for field-effect transistors. Here, using first-principles density functional calculations, we investigate the competition between Peierls instability and spin orderings in zigzag graphene nanoribbons carved in a fully hydrogenated graphene (graphane) as a function of their width N (the number of zigzag C chains composing a nanoribbon). We find that such a nanoribbon with N = 1 undergoes a Peierls instability caused by a strong electron lattice coupling, leading to a band-gap opening. For N >= 2, the Peierls instability is significantly weakened or disappears because of the interaction of zigzag C chains, whereas a ferromagnetic spin ordering on each side is stabilized by the formation of the localized edge states. We find that the spins on both sides are further stabilized with their antiparallel alignments, accompanying the band gap opening. Therefore, ultranarrow zigzag graphene nanoribbons carved in graphane are semiconducting as a consequence of a Peierls instability or an antiferromagnetic spin ordering between the two edges which is useful for the application of field-effect transistors.