Exact solutions to the tight - binding model forthe conductance of carbon nanotubesHyoung

We solve the Green's equation exactly for the armchair-type carbon nanotubes with the one-electron tight-binding Hamiltonian and obtain analytic expressions for the conductance of the nanotube with local perturbations. Our results explicitly show the dependence of the conductance on the Fermi level, the tubular radius, and the strength of the perturbation. A carbon nanotube is a new form of graphitic carbon discovered by Iijima 1] in carbon rods after an arc discharge in 1991. The electronic structure of the tube can usually be regarded as that of a graphite sheet with the periodic boundary condition along the circumference directionn2]. Nanotubes show metallic or semiconducting behaviors depending very sensitively on their radii and helical structures. Among various geometrical shapes, the armchair-type (n; n) carbon nanotube is metallic with two linear bands crossing at the Fermi levell2]. Due to these two bands, the conductance of the armchair-type nanotube is predicted to be 2(2e 2 =h) for small bias voltage according to the Landauer formulaa3,4]. The quantum conductance of carbon nanotubes has been studied previously using various theoretical methods 5{7]. In the present work, we shall derive the exact form of the Green's function in the armchair-type carbon nanotube and present analytic expressions for the conductance revealing the functional dependence of the conductance on the Fermi level, the tubular radius, and the strength of perturbations. Since the electronic states near the Fermi level in a carbon nanotube come mainly from p-orbitals perpendicular to the graphitic surface, the motion of electrons at the energy is well described by the tight-binding Hamiltonian with one-electron per atom where only the nearest-neighbor hopping matrix