Effects of finite length on the electronic structure of carbon nanotubes

The electronic structure of finite-length armchair carbon nanotubes has been studied using several ab-initio and semiempirical quantum computational techniques. 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 the band-gap decreases with increasing tube length; however, the decrease is not monotonic but shows a well-defined oscillation in short tubes. This oscillation can be explained in terms of periodic changes in the bonding characteristics 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) system to that characteristic of a delocalized one-dimensional (1-D) system. This 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.