Electron transport properties of incommensurate double-walled carbon nanotubes

An efficient way is developed to calculate the matrix elements of Green’s functions in real space, by which conductances of the long clean incommensurate double-walled carbon nanotubes (DWNTs) are calculated. It is shown that, in a certain lower energy region, the conductances keep 2G0 except for at a few energy positions for the system length at least up to about 1.4 μm, and when the tube length increasing to be 10 μm order, the conductance tend to be 1G0, which is in good consistency with the experiments. The electron motion in the other higher energy regions becomes nonballistic.