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Figure 11
(a) Graphene is a 2D structure made of a honeycomb lattice of carbon atoms (in black on the picture). The standard primitive hexagonal lattice is generated by the pair [1,j = \exp({2i\pi/3})] in complex notations defining the unit cell drawn in gray. The point symmetry group is 6m which can be generated by the two mirrors M and [M^{\prime}]. (b) Generating coincidence lattices by rotation is easily obtained by applying rotations α around the origin that superpose nodes deduced from each other by the mirror along the real axis transforming the node [n+\bar{j}m] into n+jm. Because of the hexagonal symmetry, choosing point [n+\bar{j}m] with n,m coprime in the region [n\,\gt\,2m\,\gt\,0] between the mirrors M and [M^{\prime}] is sufficient for generating all the possible rotations of coincidence angles α and [\pi/3-\alpha].

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ISSN: 2053-2733
Volume 79| Part 4| July 2023| Pages 301-317
https://doi.org/10.1107/S2053273323003662
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