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 Hückel 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 $0.001e^{-}/\text{atom}$ 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 $\sigma \text{−}\pi$ mixing in such small diameter tubes.

Figure 1

(Color online) LDA band structure of the (7,0)@(16,0) DWCNT in comparison with the band structures of the subsystems in isolated single geometry (the Fermi levels are all shifted to 0 eV). $c$ is the lattice constant of the nanotubes.

Figure 2

(Color online) LDA band structure of the (8,0)@(17,0) DWCNT in comparison with the band structures of the subsystems in isolated single geometry (the Fermi levels are all shifted to 0 eV). $c$ is the lattice constant of the nanotubes.

Figure 3

Charge transfer density along the tube axis versus the diameter difference $\left(\Delta d\right)$ between the inner and outer tubes of DWCNTs according to the IMH model (the inner tubes are always negatively charged). The straight line is a linear regression (see text).

Figure 4

Comparison between the IMH and LDA results for the charge transfer in DWCNTs. The CT values obtained from the VASP calculations by analyzing the Bader charges (solid) agree well with those obtained from the SIESTA calculations by Mulliken population analysis (circles), but both of them give a smaller value than the IMH method (dashed). The eight points of the VASP and IMH calculations correspond to (4,4)@(9,9), (5,5)@(10,10), (6,6)@(11,11), (6,4)@(12,8), (7,0)@(16,0), (8,0)@(17,0), (9,0)@(18,0), and (8,2)@(16,4) from left to right. For SIESTA, only the achiral DWCNTs are plotted (see text).

Figure 5

(Color online) Charge redistribution profile (change of the electron density caused by interlayer interaction) in the case of the (8,0)@(17,0) DWCNT in one of the planes perpendicular to the tube axis containing the atoms (arbitrary units). The LDA results agree well with previous calculations (Ref. 16), while the IMH results show a more localized redistribution profile owing to the neglect of $s\text{−}p$ mixing (see text).

Figure 6

(Color online) Charge redistribution profile (change of the electron density caused by interlayer interaction) in the case of the (6,6)@(11,11) DWCNT in one of the planes perpendicular to the tube axis containing the atoms (arbitrary units).

Figure 7

(Color online) LDA charge redistribution profile (change of the electron density caused by interlayer interaction) in the case of the (14,0)@(23,0)@(32,0)@(41,0) MWCNT in one of the planes perpendicular to the tube axis containing the atoms (arbitrary units).

Figure 8

(Color online) LDA charge redistribution profile (change of the electron density caused by interlayer interaction) in the case of the (5,0)@(14,0)@(23,0)@(32,0)@(41,0) MWCNT in one of the planes perpendicular to the tube axis containing the atoms (arbitrary units).