Unique effects of incommensurability on transport properties of incommensurate double-walled carbon nanotubes

On the basis of the multichannel Landauer formula, we investigated the effects of incommensurability on the electron transport properties of clean incommensurate double-walled carbon nanotubes (DWNTs). The results obtained clearly show that electron transport in incommensurate DWNTs can be either ballistic or non-ballistic depending on the energy region. In the lower energy region, the conductances remain at 2G(0) (where G(0) = 2e(2) / h is the conductance quantum) except for at a very few positions, at least up to the system length of about 1.4 mum. And with increasing length, the conductances tend to change from 2G(0) to 1G(0) due to the antiresonances. This offers a possible explanation for the measurement results reported by Frank et al (1998 Science 280 1744) and by Urbina et al (2003 Phys. Rev. Lett. 90 106603). In the other energy regions, electron transport is non-ballistic and the conductances show a power law decay.