Systematicab initiostudy of the optical properties of BN nanotubes

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 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 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 \^{}z), the absorptive part ^'' 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). In other words, in the low-energy region (4--90. 3em{0ex}eV) the ^'' consists of a single distinct peak at 5. 50. 3em{0ex}eV, and in the high-energy region (9--250. 3em{0ex}eV) it exhibits a broad peak centered near 14. 0 eV. For the electric field perpendicular to the tube axis (E \^{}z), the ^'' spectrum of all the nanotubes (except the ultrasmall-diameter nanotubes) in the low-energy region also consists of a pronounced peak at 6. 00. 3em{0ex}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 \^{}z, showing a moderate optical anisotropy in the nanotubes that is smaller than in h-BN. Interestingly, the static dielectric constant (0) for all the nanotubes is almost independent of diameter and chirality with (0) for E \^{}z being only about 30% larger than for E \^{}z. For both electric-field polarizations, the static polarizability (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 of h-BN, being dominated by a broad +-electron plasmon peak at 260. 3em{0ex}eV and a small -electron plasmon peak at 70. 3em{0ex}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.