In this Demonstration, the width index
and the chiral index
can be varied independently to allow investigating band structures for the tubes and ribbons with different lateral sizes. As discussed in , band structures that match at the center
and at the edge
of the dimensionless Brillouin zone can be obtained when
, respectively. Choose the "full" comparison mode to overlay the two electronic band structures. In this mode, it is seen that, unlike the case of armchair graphene nanoribbons and zigzag carbon nanotubes , for a zigzag ribbon and armchair tube the band matching cannot be achieved in the whole Brillouin zone.
In all modes of comparison, the bands are explicitly numbered as proposed in . You can choose "inverse" or "direct" band enumeration. Since some of the bands for ACNTs are double degenerate, they are labeled with two numbers, with one number enclosed in parentheses.
For ZGNRs, the transition points
are defined via the width index
The energy band matching presented here for armchair tubes and zigzag ribbons has been predicted to result in peak correlation of the optical absorption spectra in the tubes and ribbons . This prediction may soon be tested experimentally, since atomically precise zigzag edges have recently been produced through surface-assisted polymerization and cyclodehydrogenation of specifically designed precursor monomers .
energy band matching in the Brillouin zone center
energy band matching at the Brillouin zone edge
Snapshot 3: comparison of
energy bands in the "full" mode
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