Band Structures in Zigzag Graphene Nanoribbons and Armchair Carbon Nanotubes
Band Structures in Zigzag Graphene Nanoribbons and Armchair Carbon Nanotubes
This Demonstration compares electronic band structures of zigzag graphene nanoribbons (ZGNRs) with those of armchair carbon nanotubes (ACNTs) [1]. In the nearest-neighbor tight-binding model, the dimensionless electron energy , where is the hopping integral, is plotted against the dimensionless electron wavenumber . This plot is supplemented by the tube and ribbon atomic structures. Positions of the points corresponding to the Dirac points in the graphene Brillouin zone are marked by red vertical lines labeled and . For ZGNRs, the gray vertical lines designate positions of the transition points and ', where ribbon energy bands sneak outside the light blue area corresponding to the region of the graphene band structure. For both ZGNRs and ACNTs, the band indices are specified for all their bands.
E/γ
γ
k∈(-π,π)
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K
K'
k
t
k
t
J