Electron scattering by impurities in a carbon nanotube near boundary points of subbands

• We study the scattering problem for the zigzag carbon nanotube.
• The Green function for the carbon nanotube was found explicitly.
• We obtain the general approximate expression for the transmission probability.
• Reflection can be large for the small potential and the electron velocity.
• We found the condition when the transmission probability is close to unity.

We study, within the tight-binding approximation, the scattering problem for the Hamiltonian of the carbon nanotube with the non-local impurity potential. The Green function of the non-perturbed Hamiltonian was found explicitly. In the case where the potential and the electron velocity are small, we obtained a simple expression for the transmission probability. The scattering occurs mainly in the two subbands. The transmission probability increases by increasing the diameter of a carbon nanotube, or when the Fermi energy tends to zero. We found the condition when the transmission probability is close to unity.