Phonon eigenvectors of chiral nanotubes

Although a commonly neglected fact, the physical properties of chiral carbon nanotubes may differ significantly from those of the usually considered, simpler achiral tubes. We show that the phonon eigenvectors, e.g., of the high-energy eigenmodes no longer fall into axial and circumferential modes as in armchair and zig-zag nanotubes. The atomic displacement may, instead, point in any tangential direction and even show an angular dependence of its direction around the circumference, as the results of ab initio calculations demonstrate.