Folded graphene nanoribbons with single and double closed edges

Graphene nanoribbon folds with single and double closed edges are studied using density functional theory methods. The van derWaals dispersive interactions are included via semiempirical pairwise optimized potential. The geometrical phases of the single and double folded ribbons are obtained. The electronic structure in terms of energy needed for the folding process, van der Waals contribution, energy band gaps, and band structures are also calculated. The results are interpreted in terms of peculiarities of the structures and dispersion interactions. It is shown that significant modifications in the electronic structure can be achieved as a result of folding.