Bend-induced insulating gap in carbon nanotubes

The effect of uniform bend on the electronic structure of single wall carbon nanotubes is investigated as function of diameter, chirality, and plane of bend. This deformation can only mix states with the same projection of $\mathbf{k}$ on the tube’s axis and belonging either to one nanotube line or to nearest neighbor and next nearest neighbor lines. The bend-induced insulating gap opens in chiral and zigzag tubes, scales as the square of the bend curvature and is strongly dependent on the chirality of the tube. For large diameters of the tubes, the bend-induced gap scales as the square of the tube’s diameter and is strongly determined by the changes of the bond lengths. The observation of these gaps should become possible with current experimental techniques.