  Graphene nanoribbons are semiconductor nanostructures with great potentials
in nanoelectronics. Their realization particularly with small lateral
dimensions below a few nanometers, however, remains challenging. Here we
theoretically analyze zig-zag graphene nanoribbons created in a graphane
substrate (a fully saturated two-dimensional hydrocarbon with formula CH) and
predict that they are stable down to the limit of a single carbon chain. We
exploit density functional theory with B3LYP functional that accurately treats
exchange and correlation effects and demonstrate that at small widths below a
few chains these zig-zag nanoribbons are semiconducting due to the Peierls
instability similar to the case of polyacetylene. Graphene nanoribbons in
graphane might represent a viable strategy for the realization of ultra-narrow
semiconducting graphene nanoribbons with regular edges and controlled chemical
termination and open the way for the exploration of the competition between
Peierls distortion and spin effects in artificial one-dimensional carbon
structures.
