Effects of finite length on the electronic structure of carbon nanotubes

The electronic structure of finite-length armchair carbon nanotubes has bee n studied using several ab-initio and semiempirical quantum computational t echniques. The additional confinement of the electrons along the tube axis leads to the opening of a band-gap in short armchair tubes. The value of th e band-gap decreases with increasing tube length; however, the decrease is not monotonic but shows a well-defined oscillation in short tubes. This osc illation can be explained in terms of periodic changes in the bonding chara cteristics of the HOMO and LUMO orbitals of the tubes. Finite-size graphene sheets are also found to have a finite band-gap, but no clear oscillation is observed. As the length of the tube increases the density of states (DOS ) spectrum evolves from that characteristic of a zero-dimensional (0-D) sys tem to that characteristic of a delocalized one-dimensional (1-D) system. T his transformation appears to be complete already for tubes 10 nm long. The chemical stability of the nanotubes, expressed by the binding energy of a carbon atom, increases in a similar manner.