Reflection by defects in a tight-binding model of nanotubes

Abstract

We use a transfer-matrix method to study defects in a tight-binding model of carbon nanotubes. We calculate the reflection coefficient R for a simple barrier created by a pointlike defect of strength E in armchair ${(N}_{a}{,N}_{a})$ and zigzag ${(N}_{a},0)$ nanotubes for the whole range of energy $\ensuremath{\omega}$ and arbitrary number of conducting channels. We find that R scales at the Fermi level (i.e., $\ensuremath{\omega}=0)$ as ${R=s(E/t)}^{2}{/N}_{a}^{2}$ $(t$ being the hopping parameter), where $s\ensuremath{\approx}1/6$ (for the armchair nanotubes) and $s\ensuremath{\approx}1/2$ (for the zigzag nanotubes). We also perform a similar calculation for a ``5-77-5'' defect and find the results to be like the ones obtained for a strong point defect with $E=6t$.