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. 2019 Mar 13;6(3):181605. doi: 10.1098/rsos.181605

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© 2019 The Authors.

Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.

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Figure 1. — The crystal and band structure of SWCNTs. (a) Real space and (b) reciprocal space representation of the hexagonal lattice of 2D graphene. a_C–C; is the carbon–carbon bond length. a_1,2 and b_1,2 are the primitive unit vectors in real and reciprocal space, respectively. The dashed line parallelogram defines the unit cell of graphene with two different carbon atoms A and B. High-symmetry points in reciprocal space, Γ, M and K, are labelled in the 1st Brillouin zone. (c) A chiral vector C of a SWCNT, defined on the graphene sheet as a linear combination of a₁ and a₂ with integer coefficients. An index (n,m) represents SWCNT chirality. Different index combinations result in either (d) a metallic SWCNT or (e) a semiconducting SWCNT.