Localization in carbon nanotubes within a tight-binding model

Abstract

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 $\ensuremath{\xi}(\ensuremath{\omega})$ as a function of energy \ensuremath{\omega}. Comparison of $\ensuremath{\xi}(0)$ 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 $\ensuremath{\xi}(0)\ensuremath{\approx}{3l}_{\mathrm{mfp}}=3\ifmmode\times\else\texttimes\fi{}{3aN}_{a}{t}^{2}{/2\mathrm{cE}}^{2}$ $(t$--- hopping integral, $a$--- lattice constant).