Bandgaps of bent and buckled carbon nanotubes

Abstract

Carbon nanotube's large electro-mechanical coupling and robustness makes them attractive for applications where bending and buckling is present. But the nature of this coupling is not well understood. Existing theory treats only weak and homogeneous deformations. We generalize it and derive close-form expressions for bandgaps under non-homogeneous deformation. The theory is first compared with a number of published DFT simulations, and then applied to the specific case of bending and buckling -- where a kink is present. In the pre-buckling regime, bandgaps change $\propto\pm \kappa^4$ where $\kappa$ is the bending curvature; inside the kink at post-buckling, while near criticality, the kink is shallow and the gap is $\propto \pm\kappa^{1/2}$, where the sign depends on the chiral integers. For a deeper kink but still with an open cross-section, both the bandgap and local Fermi energy strongly downshift.