Subbands in Carbon Nanotubes under Radial Deformation

Carbon nanotubes, which consist of only carbon atoms, were first discovered by Iijima [1] and can be thought of as a single layer of graphite that is wrapped into a cylinder. The cylindrical nanotubes are very stable and are regarded as the strongest fibers ever; nanotubes are extremely rigid to distortions along the tube axis whereas they are very flexible to those perpendicular to the axis [2]. The electronic structure of a perfect nanotube is known to be either metallic or semiconducting [2–6], depending on both the tube diameter and the wrapping index (n, m), where n and m describe the projection of the circumferential vector onto the basis vectors of the graphite lattice. Armchair (n, n) nanotubes have a band degeneracy between the so-called π and π∗ bands, which are even and odd under mirror symmetry operations. Since these two bands cross at the Fermi level, armchair nanotubes exhibit metallic conduction. In (n, m) nanotubes, where n−m is a multiple of 3, a small gap appears due to the curvature effect; in all others, a large gap appears. Recently, a field-effect transistor based on an individual nanotube molecule was demonstrated [7], and single-electron tunneling and resonant tunneling effects through single molecular orbitals was observed [8,9], indicating that nanotubes are promising materials for future molecular devices. In nanotube-based devices, nanotubes undergo various deformations from the perfect cylindrical form. Nanotubes bent by the tip of an atomic force microscope or by crossing over electrodes undergo mechanical deformations that flatten the tubes (see Fig. 1). Many prototype devices made of carbon nanotubes inevitably contain defective regions because metal-nanotube, tip-nanotube, and nanotube-substrate interactions introduce structural distortions, such as bends, twists, and kinks [7–13]. Thus, understanding the effect of mechanical deformations on the electronic structure and the transport prop-