  Geometric and electronic properties of folded graphene nanoribbons (FGNRs)
are investigated by first-principles calculations. These properties are mainly
dominated by the competition or cooperation among stacking, curvature and edge
effects. For the zigzag FGNRs, the more stable structures are revealed to be AB
stackings, while for the armchair types, AA" stackings are more stable. The
interlayer interactions and hybridization of four orbitals lead to smaller
energy gaps, anti-crossing bands, and more band-edge states. Specifically, the
broken mirror symmetry in the odd-AB stacked zigzag FGNRs is responsible for
the spin-up and spin-down splitting subbands. All FGNRs are direct-gap
semiconductors except that the edge-edge interactions cause the even-AA stacked
zigzag FGNRs to exhibit a pair of metallic linear bands. The width-dependent
energy gaps in the armchair FGNRs can be classified into six groups.
Furthermore, there exist rich features in density of states, including the
form, number, intensity and energy of the special structures.
