Lowest Lyapunov Exponents for the Armchair Nanotube

#### C. Dobrovolny, T.C. Dorlas, J.V. Pule

2007, v.13, Issue 2, 331-390

ABSTRACT

We compute sum of the two the lowest Lyapunov exponents $\gamma_{2N-1} + \gamma_{2N}$ of a tight-binding model for an single-wall armchair carbon nanotube with point impurities to lowest (second) order in the disorder parameter $\lambda$. The result is that $\gamma_{2N-1} + \gamma_{2N} \sim \lambda^2 N^{-1}$, where $N$ is the number of hexagons around the perimeter. This is similar to the result of Schulz-Baldes [H. Schulz-Baldes, Perturbation theory for Lyapunov exponents of an Anderson model on a strip, Geom. and Funct. Anal., 2004, v. 14, 1089-1117] for the standard Anderson model on a strip, but because there are only two conducting channels near the Fermi level (centre of the spectral band), this implies that the scattering length is proportional to the diameter of the tube as predicted by Todorov and White [C.T. White and T.N. Todorov, Carbon nanotubes as long ballistic conductors, Nature, 1998, v. 393, 240-242].

Keywords: Anderson localization,carbon nanotube,ballistic transport,tight-binding model