The atomic structures of graphene nanoribbons and an folded graphene nanoribbons. Top view of the perfect zigzag (a) and armchair (b) graphene nanoribbons, and the width of C atomic lines for zigzag and armchair are NZ and NA, respectively. (c) Side view of the initial folded graphene nanoribbons, which contains a fraction of nanotube in closed edge and two flat sheets in open edges. The symbol D denotes the initial distance between the upper and bottom flat sheets. (d) Side view of the relaxed folded graphene nanoribbons. The symbol Dmax represents the distance between the maximum distance for the curved part and Dmin is the distance between the two flat layers. (e) Top view of the four different stacking styles for the folded graphene nanoribbons, and such zone is shown in the red dashed box in (c): (I) AA-stacking, (II) AB-stacking, (III) AB′-stacking, and (IIII) AB″-stacking. The open edges are saturated with hydrogen atoms in white balls, while others are C atoms.
The final configurations of zigzag folded graphene nanoribbons as a function of the initial structures. (a), (b), and (c) for the even number of carbon chain with width NZ = 40, while (d), (e), and (f) for the odd number of carbon chain with width NZ = 41; (a) and (d) show the relationship between the final stacking styles and initial stacking styles in different initial distance D; (b) and (e) exhibit that the maximum distance Dmax in the bending portion and the minimum distance Dmin between the upper and bottom layers as a function of the initial distance D; The formation energy of zigzag folded graphene nanoribbons as a function of initial distance D are shown in (c) and (f) for NZ = 40 and NZ = 41, respectively. The four typical stacking styles AB, AB, AB′, and AB″ are considered in our calculations.
The final structures and the formation energy of armchair folded graphene nanoribbons with various different initial distances, D. (a) The final structures of the Dmax (left-axis) and Dmin (right-axis) for the AA- and AB′-stacking in different initial distances, D; (b) The formation energy for the AA- and AB′-stacking as a function of initial distance D. AA-stacking in red dashed line and AB′-stacking in blue short dashed line.
(a) and (b) The energy difference between the folded graphene nanoribbons and the flat ones in the same width versus the C atomic lines for thezigzag and armchair edge graphene nanoribbons, respectively.
The electronic structure of the zigzag folded graphene nanoribbons. (a),(b), (c), and (d) show the band structures for NZ = 20, NZ = 21, NZ = 40, and NZ = 41, respectively.
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