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Formation of fullerene superlattices by interlayer bonding in twisted bilayer graphene
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Image of FIG. 1.
FIG. 1.

(Color online) (a,b) Moiré patterns generated by a pair of rotated graphene layers at θ = 30° and θ = 30 ± 2.204°, respectively. The dark shaded atoms (colored blue online) are those involved in the creation of the embedded caged structures; dashed lines are used to represent the two superlattices. (c) Supercell for a θ = 30° twisted bilayer; top and side views are shown of the interlayer-bonded configurations generated. Open squares, open diamonds, and X-marks are used to denote either interlayer-bonded or hydrogenated C atoms. (d) Different views of the C48 and C72 fullerenes generated by removing the shaded (colored online) atoms from the configurations depicted in (c). Each panel in (d) depicts caged structures removed from the bilayers (left) and the corresponding relaxed structures (right). (e) Valence electron density (VED) distributions on planes normal to the surface of the pristine and bonded bilayers (top and bottom images, respectively, shown on the left) and on the planes P1, P2, and P3 parallel to the graphene layers at different distances from the top layer, as defined in (c). The VED increases as the color changes from red (zero VED) to blue. For interpretation of the references to color in the VED distributions, the reader is referred to the online version of this article.

Image of FIG. 2.
FIG. 2.

(Color online) Electronic band structures of pristine [dot-dashed (blue online) curves], hydrogenated interlayer-bonded [solid (green online) curves], and hydrogenated nonbonded [dashed (red online) curves] twisted bilayer graphene for rotation angles of (a,b) θ = 30° and (c,d) θ = 30 ± 2.204°. The band diagrams of the hydrogenated structures correspond to the relaxed configurations with hydrogenation pattern (a,c) (A) and (b,d) (F), which generate embedded C48 and C72 caged configurations, respectively. The energies are plotted as functions of wave number along the path in the first BZ shown in the inset in (a).

Image of FIG. 3.
FIG. 3.

(Color online) (a–i) Embedded caged structures formed by interlayer C-C bonding in a θ = 30° twisted bilayer, containing different numbers of C atoms (NAT) and interlayer C-C bonds (NIB). The atoms involved in the creation of the interlayer-bonded configurations are marked on the top part of each panel and different views of the removed and relaxed fullerenes are depicted on the bottom: (a) C78, (b) C100, (c) C108, (d) C130, (e) C160, (f) C182, (g) C138, (h) another C160, and (i) C190.


Generic image for table
Table I.

Binding energies for interlayer-bonded (E bb ) and nonbonded (E bn ) structures of θ = 30° and 30 ± 2.204° twisted bilayer graphene for different numbers of chemisorbed H atoms, N H , and different hydrogenation patterns, (A)–(G).


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Formation of fullerene superlattices by interlayer bonding in twisted bilayer graphene