Systematicab initiostudy of the optical properties of BN nanotubes

Abstract

A systematic ab initio study of the optical and electronic properties of BN nanotubes within density functional theory in the local density approximation is performed. Specifically, the optical dielectric function $\ensuremath{\epsilon}$ and the band structure of the single-walled zigzag [(5,0),(6,0),(9,0),(12,0),(15,0),(20,0),(27,0)], armchair [(3,3),(4,4),(6,6),(8,8),(12,12),(15,15)], and chiral [(4,2),(6,4),(8,4),(10,5)] as well as the double-walled zigzag (12,0)@(20,0) BN nanotubes are calculated. The underlying atomic structure of the BN nanotubes is determined theoretically. It is found that though the band gap of all the single-walled nanotubes with a diameter larger than 15 \AA{} is independent of diameter and chirality, the band gap of the zigzag nanotubes with smaller diameters decreases strongly as the tube diameters decrease and that of the armchair nanotubes has only a weak diameter dependence, while the band gap of the chiral nanotubes falls in between. It is also found that for the electric field parallel to the tube axis $(E\ensuremath{\Vert}\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{z})$, the absorptive part ${\ensuremath{\epsilon}}^{\ensuremath{''}}$ of the dielectric function for all the nanotubes except a few with very small diameters, is very similar to that of bulk hexagonal (h) BN with the electric field parallel to the BN layers $(E\ensuremath{\perp}c)$. In other words, in the low-energy region $(4--9\phantom{\rule{0.3em}{0ex}}\mathrm{eV})$ the ${\ensuremath{\epsilon}}^{\ensuremath{''}}$ consists of a single distinct peak at $\ensuremath{\sim}5.5\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$, and in the high-energy region $(9--25\phantom{\rule{0.3em}{0ex}}\mathrm{eV})$ it exhibits a broad peak centered near 14.0 eV. For the electric field perpendicular to the tube axis $(E\ensuremath{\perp}\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{z})$, the ${\ensuremath{\epsilon}}^{\ensuremath{''}}$ spectrum of all the nanotubes (except the ultrasmall-diameter nanotubes) in the low-energy region also consists of a pronounced peak at $\ensuremath{\sim}6.0\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$, while in the high-energy region it is roughly made up of a broad hump starting from 10.0 eV. The magnitude of the peaks is in general less than half of the magnitude of the corresponding ones for $E\ensuremath{\Vert}\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{z}$, showing a moderate optical anisotropy in the nanotubes that is smaller than in h-BN. Interestingly, the static dielectric constant $\ensuremath{\epsilon}(0)$ for all the nanotubes is almost independent of diameter and chirality with $\ensuremath{\epsilon}(0)$ for $E\ensuremath{\Vert}\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{z}$ being only about 30% larger than for $E\ensuremath{\perp}\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{z}$. For both electric-field polarizations, the static polarizability $\ensuremath{\alpha}(0)$ is roughly proportional to the tube diameter, suggesting that, unlike carbon nanotubes, the valence electrons on the BN nanotubes are tightly bound. The calculated electron energy-loss spectra of all the nanotubes studied here for both electric field polarizations are similar to those of $E\ensuremath{\perp}c$ of h-BN, being dominated by a broad $\ensuremath{\pi}+\ensuremath{\sigma}$-electron plasmon peak at $\ensuremath{\sim}26\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ and a small $\ensuremath{\pi}$-electron plasmon peak at $\ensuremath{\sim}7\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. Interwall interaction is found to reduce the band gap slightly and to have only minor effects on the dielectric functions and energy-loss spectra. The calculated dielectric functions and energy-loss spectra are in reasonable agreement with the available experimental data.