Reflection by defects in a tight-binding model of nanotubes

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 $\omega$ and arbitrary number of conducting channels. We find that R scales at the Fermi level (i.e., $\omega =0)$ as ${R=s(E/t)\mathrm{}}^2{/N}_a^2$ $(t$ being the hopping parameter), where $s\approx 1/6$ (for the armchair nanotubes) and $s\approx 1/2$ (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 $E=6t$.