WOLFRAM|DEMONSTRATIONS PROJECT

Band Structures in Zigzag Graphene Nanoribbons and Armchair Carbon Nanotubes

​
compare Brillouin zone
center
edge
full
band enumeration
direct
inverse
ribbon width index, w
1
2
3
4
5
6
tube chiral index, n
1
2
3
4
5
6
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
E/γ
, where
γ
is the hopping integral, is plotted against the dimensionless electron wavenumber
k∈(-π,π)
. This plot is supplemented by the tube and ribbon atomic structures. Positions of the
k
points corresponding to the Dirac points in the graphene Brillouin zone are marked by red vertical lines labeled
K
and
K'
. For ZGNRs, the gray vertical lines designate positions of the transition points
k
t
and
k
t
'
, 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
J
are specified for all their bands.