Continuum model for low-frequency phonons of boron nitride nanotubes

A continuum model is employed to calculate the low-frequency phonons of boron nitride nanotubes. We find an excellent agreement of the optically active modes calculated within this approach and those from more elaborate calculations within an energy and wavelength window that can be established beforehand, from the choice of the bulk input parameters. We verify that this model describes correctly the dependence of radial breathing mode with the radius, the existence of parabolic modes at small wavevectors, and other general characteristics of the dispersion relations of these systems.This work was partially supported by Spanish MINECO through Grant FIS2012-33521. D.S-P acknowledges CLAF support through grant CNPq-Brazil. R.P.-A. acknowledges CONACyT (México) support through Grant 208108 and hospitality at ICMM-CSIC, Madrid, Spain