Vibrational properties of boron-nitride nanotubes: effects of finite length and bundling

We present ab initio calculations of phonons in single-wall boron-nitride (BN) nanotubes. Raman and infrared (IR) active modes of isolated and infinitely long tubes are evaluated according to the nonsymmorphic rod groups of BN nanotubes. For tubes of finite length, the selection rules are less restrictive and give rise to additional modes, which may be observed in Raman and IR spectroscopy with an intensity depending on the tube length. Bundling of tubes is shown to have little effect on the phonon frequencies. However, arranging tubes in a large periodic array (larger than the wavelength of incoming light) gives rise to a strong frequency shift (longitudinal-optical-transverse-optical splitting) of certain modes due to the establishing of a macroscopic electric field. Modes of A₁ symmetry experience a shift for laser light along the tube axis and E₁ modes are split for light incidence in the perpendicular direction.