Systematic and efficient band tracing for chiral CNTs via natural helical crystal lattice model

Theoretical characterizations for carbon nanotubes (CNTs) are often confined to achiral CNTs due to the formidable size of the translational unit cell for chiral tubes. Here we use the previously proposed natural helical crystal lattice (NHCL) model to systematically investigate the band structure for chiral CNTs. In this study, we demonstrate that the NHCL model, not only more economical by orders of magnitude, gives rise to band diagrams that are a lot more compact and informative with respect to those evaluated by the translational crystal lattice model. Using this approach, CNTs belonging to the same “chirality family” exhibit strong correlation in the band structure which may be expanded to reproduce, with a clear interpretation, the band diagram in the minimal helical crystal lattice model.