Localization in carbon nanotubes within a tight-binding model

We analyze the influence of defects on conductance, density of states, and localization in ${(N}_a{,N}_a)$ armchair carbon nanotubes within a tight-binding model. Using the transfer-matrix method, we calculate the reflection (related to the conductance) from a sequence of defects and relate its energy dependence near the Fermi level to the appearance of a quasibound state. This state is also seen in the density of states and in the energy dependence of the quasiparticle lifetime. We compute the localization length $\xi \left(\omega \right)$ as a function of energy ω. Comparison of $\xi \mathrm{}\left(0\right)\mathrm{}$ with the mean free path $l_{\mathrm{mfp}}$ in the limit of small defect concentration $c$ and small defect strength $E$ leads to a simple approximate relation $\xi \mathrm{}\left(0\right)\mathrm{}\approx {3l}_{\mathrm{mfp}}=3\mathrm{}\times {3aN}_a{t}^2{/2\mathrm{cE}}^2$ $(t$— hopping integral, $a$— lattice constant).