Linear optical properties of zigzag single-walled BN nanotube ensembles from a model calculation

Abstract

We present a simple theoretical description of the linear optical properties of zigzag single-walled BN nanotube (BN-SWNT) ensembles within a single-particle approach that uses the Kr\'al-Mele-Tom\'anek effective Hamiltonian for modeling the electronic structure of such tubes. The perturbation-theory method of Genkin and Mednis is applied to derive analytical expressions for both the real and imaginary parts of the linear optical susceptibility ${\ensuremath{\chi}}^{(1)}(\ensuremath{\omega})$, and these are used to calculate numerically the optical functions (dielectric function, refractive index, reflectance and optical absorption coefficient) for several representative BN-SWNT ensembles. The results of our calculations are discussed in the light of the recent experimental observation by Lauret et al. [Phys. Rev. Lett. 94, 037405 (2005)] of the optical absorption spectrum of an assemble of large-diameter BN-SWNT's. It is shown that the developed theory is capable of explaining the dominant features of the experimental data, thus suggesting that the characteristic peaks observed in the optical absorption spectrum of BN-SWNT's are due to direct interband electron transitions between pairs of van Hove singularities in the electronic density of states of these tubes.