Bandgaps of bent and buckled carbon nanotubes

TL;DR

This paper develops a generalized theory for the bandgaps of bent and buckled carbon nanotubes, accounting for non-homogeneous deformations and providing explicit formulas validated against simulations.

Contribution

It introduces a new analytical framework for understanding how bending and buckling affect nanotube electronic properties, extending beyond previous weak deformation models.

Findings

Bandgaps vary as ±κ⁴ in pre-buckling regimes.

Near critical buckling, bandgaps scale as ±κ^{1/2}.

Deeper kinks cause significant downshifts in bandgap and Fermi energy.

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.