Lattice vibrations of a single-wall boron nitride nanotube

We construct a simple model which describes the lattice dynamics of a single-wall boron nitride nanotube. The model includes short-range interactions between nearest and second-nearest neighbors as well as long-range Coulomb interactions between polar atoms. It is clearly shown that flexure modes exist in boron nitride nanotubes consisting of polar atoms. We also find that the frequency of the radial breathing mode is inversely proportional to the tube radius R and that the lowest optical mode displays the radius dependence of 1/ R2 consistent with earlier calculations.