Intrinsic edge asymmetry in narrow zigzag hexagonal heteroatomic nanoribbons causes their subtle uniform curvature

The atomic and electronic structure of narrow zigzag nanoribbons with finite length, consisting of graphene terminated by fluorine on one side, hexagonal (h) h-BN, and h-SiC were studied with density functional theory. It is found that the asymmetry of nanoribbon edges causes a uniform curvature of the ribbons due to structural stress in the aromatic ring plane. Narrow graphene nanoribbons terminated with fluorine on one side demonstrate a considerable out-of-plane bend, suggesting that the nanoribbon is a fraction of a conical surface. It is shown that the intrinsic curvature of the narrow nanoribbons destroys the periodicity and results in a systematic cancellation of the dipole moment. The in- and out-of-plane curvature of thin arcs allows their closure in nanorings or cone fragments of giant diameter. Using the fragment molecular orbital method, we optimized the structure of a planar giant arc and a closed ring of h-BN with a diameter of 105 nm.