Static polarizabilities of single-wall carbon nanotubes

The static electric polarizability tensor of single-wall carbon nanotubes is calculated within the random-phase approximation using a simple tight-binding model and a classical correction to include local fields. We find that the polarizability for constant fields parallel to the cylindrical axis is highly dependent on the details of the tube's electronic structure. In contrast, the polarizability for fields perpendicular to the axis only depends on the tube radius. The relative magnitudes of these two quantities suggests that under the application of a randomly oriented electric field, nanotubes acquire dipole moments pointing mainly along their axes, with the size of the dipole inversely proportional to the square of the minimum direct band gap