Dynamic dielectric response and electron-energy-loss spectra of individual single-walled BN nanotubes

Motivated by the recent electron-energy-loss-spectroscopy (EELS) experiment of Arenal [Phys. Rev. Lett. 95, 127601 (2005)], we investigate the collective pi-electronic excitations in individual boron nitride single-walled nanotubes (BN-SWNTs) with a zigzag wrapping. The dynamic dielectric response of such tubes is treated within a self-consistent-field approach using the one-particle states of the pi-electron system of the BN-SWNTs derived from a simple two-band tight-binding model. Based on this approach, we obtain explicit analytic expressions for the real and imaginary parts of the frequency- and wave-number-dependent dielectric function of the system, whereby the electron-energy-loss function can easily be calculated. Numerical results for this function are presented for several zigzag BN-SWNTs in order to illustrate the possible electron-energy-loss spectra, and each tube is found to support only one branch of the wave-number-dispersed collective pi-plasmon mode for each transferred quantum angular momentum L. In this respect, our results are in good agreement with the experiment, where only one pronounced peak, which can presumably be attributed to the pi-plasmon excitations with a small L and a small transferred momentum q, dominates the electron-energy-loss spectra in the range up to 8 eV. The wave-number dispersion of the plasmon modes with different L's is extracted from the calculated spectra of the real part of the dielectric function, and it is shown that the plasmon dispersion curves exhibit a number of unusual characteristics that could be observable in momentum-resolved EELS experiments.