Twisting Effects on Carbon Nanotubes: A First-Principles Study with Helical Symmetry Operations

We report the energetics and the electronic properties of twisted carbon nanotubes (CNTs). We use a real-space density functional theory with helical-symmetry operation, and apply it for several CNTs with the diameters of around 0.8 nm including the experimentally abundant (6,5) nanotube. By using this computational code, one can now obtain the total energies with enough accuracies to optimize the CNT geometries including quasi-continuous twisting levels for any type of nanotube in principle. As a result, it is found that chiral nanotubes possess twisted geometries at their ground states. The electronic structures of CNTs depend sensitively on twisting levels in this diameter region, and the twisting effects on their fundamental gap values can be judged by the value of mod(n - m, 3), where n and m are the chiral indices.