Edge effects in finite elongated carbon nanotubes

The importance of finite-size effects for the electronic structure of long zigzag and armchair carbon nanotubes is studied. We analyze the electronic structure of capped (6,6), (8,0), and (9,0) single walled carbon nanotubes as a function of their length up to 60 nm, using a divide and conquer density functional theory approach. For the metallic nanotubes studied, most of the physical features appearing in the density of states of an infinite carbon nanotube are recovered at a length of 40 nm. The (8,0) semi-conducting nanotube studied exhibits pronounced edge effects within the energy gap that scale as the inverse of the length of the nanotube. As a result, the energy gap reduces from the value of ~1 eV calculated for the periodic system to a value of ~0.25 eV calculated for a capped 62 nm long CNT. These edge effects are expected to become negligible only at tube lengths exceeding 6 micrometers. Our results indicate that careful tailoring of the nature of the system and its capping units should be applied when designing new nanoelectronic devices based on carbon nanotubes. These conclusions are expected to hold for other one-dimensional systems such as graphene nanoribbons, conducting polymers, and DNA molecules.