Inter-shell interaction in double walled carbon nanotubes: charge transfer and orbital mixing

Recent nuclear magnetic resonance measurements on isotope engineered double walled carbon nanotubes (DWCNTs) surprisingly suggest a uniformly metallic character of all nanotubes, which can only be explained by the interaction between the layers. Here we study the inter-shell interaction in DWCNTs by density functional theory and inter-molecular H\"uckel model. We find charge transfer between the layers using both methods. We show that not only does the charge transfer appear already at the fundamental level of the inter-molecular H\"uckel model, but also that the spatial distribution of the change in the electron density is well described already at this level of theory. We find that the charge transfer between the walls is on the order of 0.001 e/atom and that the inner tube is always negatively charged. We also observe orbital mixing between the states of the layers. We find that these two effects combined can in some cases lead to a semiconductor--to--metal transition of the double walled tube, but not necessarily in all cases.