Static polarizability of carbon nanotubes: ab initio independent-particle calculations

An ab initio study of the static polarizability of the carbon nanotubes within density functional theory in local density and independent-particle approximations has been performed. Full-potential projected augmented wave method was used. Specifically, the static dielectric function ε(0) and electric polarizability α(0) of a number of the armchair [(3,3),(5,5),(10,10),(15,15),(20,20)], zigzag [(5,0),(10,0),(15,0),(16,0),(20,0)] and chiral [(4,2),(6,2),(6,4),(8,4),(10,5)] carbon nanotubes have been calculated. The underlying atomic structure of the carbon nanotubes was determined theoretically. The calculated static polarizability α(0) for the nanotubes is rather anisotropic with α(0) for electric field parallel to the tube axis ( E∥ z ̂ ) being two to three times larger than that for electric field perpendicular to the tube axis ( E⊥ z ̂ ). This anisotropy is further enhanced by up to a factor of five when the depolarization effects for E⊥ z ̂ is taken into account by a classical correction. For both electric field polarizations, α(0) is roughly proportional to the square of the tube diameter, suggesting that it is independent of the chirality and the details of the electronic structure of the nanotubes.