Intershell 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 intershell interaction in DWCNTs by density-functional theory and the intermolecular H\"uckel model. Both methods find charge transfer between the inner and outer tubes. We find that the charge transfer between the walls is on the order of $0.001\phantom{\rule{0.3em}{0ex}}{e}^{\ensuremath{-}}/\text{atom}$ 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. We extend our study to multiwalled nanotubes as well, with up to six layers in total. We find similar behavior as in the case of DWCNTs: electrons tend to be transferred from the outermost layer toward the innermost one. We find a notable peculiarity in the charge transfer when the (5,0) tube is present as the innermost tube; we attribute this to the $\ensuremath{\sigma}\text{\ensuremath{-}}\ensuremath{\pi}$ mixing in such small diameter tubes.

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