Elastic light scattering from π electrons in zigzag BN single-walled nanotubes

We present a theoretical study of the Rayleigh (elastic light) scattering (RS) from π electrons in boron-nitride single-walled nanotubes (BN-SWNTs) with a zigzag achiral structure. The π-electronic band structure of the nanotubes is treated within a simple analytical model based on the tight-binding and zone-folding approximations. We provide explicit formulas for the real and imaginary parts of the linear optical susceptibility χ(1)(ω), both of which contribute to the RS cross section σ(ω). The σ(ω) spectra we have calculated for several representative BN-SWNTs (l,0) of fairly large diameters (>1.3nm) show a series of very pronounced peak structures which occur at energies corresponding to resonant π-electron transitions between the valence- and conduction-energy-subband edges, where van Hove's singularities of the joint density of (electronic) states of the nanotubes are located. It is found that the RS spectra are indicative of the underlying electronic structure of the BN-SWNTs (l,0), exhibiting radically different global resonant profiles for the nanotubes with odd l and for those with even l, and thus suggesting a way of discriminating between them in experiment. Experimental implications of a number of other findings, emerging from the present theoretical calculation of the RS spectra, are also discussed.