Static Dielectric Properties of Carbon Nanotubes from First Principles

We characterize the response of isolated single-wall (SWNT) and multiwall (MWNT) carbon nanotubes and nanotube bundles to static electric fields using first-principles calculations and density-functional theory. The longitudinal polarizability of SWNTs scales as the inverse square of the band gap, while in MWNTs and bundles it is given by the sum of the polarizabilities of the constituent tubes. The transverse polarizability of SWNTs is insensitive to band gaps and chiralities and is proportional to the square of the effective radius; in MWNTs, the outer layers dominate the response. The transverse response is intermediate between metallic and insulating, and a simple electrostatic model based on a scale-invariance relation captures accurately the first-principles results. The dielectric response of nonchiral SWNTs in both directions remains linear up to very high values of applied field.

Figure 1

Log-log plot of ${\alpha }_{\parallel }$ of zigzag SWNTs as a function of band gap. The dashed line has slope $-2$. The inset shows ${\alpha }_{\parallel }$ for large-gap SWNTs as a function of $R_0/{\Delta }_g^2$.

Figure 2

Convergence of ${\alpha }_{\perp }$ and ${\alpha }_{\perp }^b$ with respect to the size $L$ of the tetragonal unit cell for a $(5,5)$ SWNT. The point at $L=10.6\AA$ corresponds to a typical tube-tube separation in a nanotube bundle.

Figure 3

Transverse polarizabilities ${\alpha }_{\perp }$ of armchair and zigzag nanotubes as a function of ${\tilde{R}}^2$. The dashed line is the best-fit result of our semimetallic shell model; the solid line ${\alpha }_{\perp }=\frac{1}{2}{\tilde{R}}^2$ corresponds to an ideal metallic cylinder.

Figure 4

Electrostatic potential for a $(10,10)$ SWNT in an applied homogeneous transverse field $E_{\mathrm{out}}$. The electric field through the center slice is shown in the inset.