Electrical resistance due to electron–phonon interaction in finite-length carbon nanotubes

The electrical resistance of an armchair single-walled carbon nanotube (SWNT) with finite length has been calculated by the tight-binding Hamiltonian and non-equilibrium Green's function method. It is found that the resistance is linearly dependent on the tube length only when the tube length is long enough. For short tubes, the electron–phonon (e–p) scattering has a minor effect on the resistance, making a short SWNT a ballistic conductor, and the resistance oscillates with increasing tube length. The tube's chirality also affects its resistance, e.g., the resistance of a metallic zigzag (18, 0) SWNT is found to be four times smaller than that of an armchair (10, 10) SWNT even though they have almost the same diameter and tube length. Finally, we found that the low frequency twisting (TW) acoustic phonon mode dominates the tube resistance at low temperatures, but the high frequency phonons' contribution surpasses it at high temperatures.