Transverse polarizabilities of carbon nanotubes: A Hartree-Fock and density functional study

The transverse polarizabilities of carbon nanotubes are computed using Hartree-Fock (HF) and density functional theory (DFT). The results of these calculations have implications for nanoelectronics, specifically for the possibility of using nanotubes as shielding for nanoelectrical components, as the results do not support the proposed enhanced polarizability, and hence enhanced shielding, of nanotubes based on metallicity. The HF and DFT calculations are shown to be in close agreement, and this agreement is discussed. We find the polarizability per unit length depends on the square of the tube radius, and is not dependent on metallicity. The current calculations are consistent with tight binding calculations using four orbitals per carbon with regard to both trend and magnitude, but differ from some recent tight binding calculations performed using one orbital per carbon. The calculations detailed in this paper are the most elaborate to date, and settle contradictory reports in the literature.

Figure 1

The transverse polarizability of $(n,n)$, and $(n,0)$ carbon nanotubes per Å length of tube computed with $6\text{−}31{\mathrm{G}}^{*}$. The solid line is for PBE while the dashed line is for HSE.

Figure 2

The transverse polarizability of $(n,n)$, and $(n,0)$ carbon nanotubes per Å length of tube computed with STO-3G. The solid line is for PBE while the dashed line is for HF. The deviation for the smaller tubes from the main line is explained in the text.

Figure 3

The band gap for a (10,0) tube as a function of gate voltage for a field applied across split gate with a 12 Å separation between the gates computed with $6\text{−}31{\mathrm{G}}^{*}$.