Curvature-Induced Energy Band Tilting in Finite-Length Carbon Nanotubes
The near-Fermi-energy energy band structure of carbon nanotubes is given by cross-sections of the graphene Dirac cones near the K and K' points. Using second-order perturbation theory and a nearest-neighbor approximated tight-binding model, curvature-induced corrections to the graphene-based effective model are derived. In addition to the already known Dirac-point shift, the curvature is shown to cause not only a warping of the Dirac cone, tantamount to a slight compression and a correction to the overall Fermi velocity, but also a tilting of the Dirac cone and the associated nanotube energy bands. This tilting results in a velocity asymmetry for left- and right-going waves and two different kinds of excitations, allowing for varying degeneracy in the same sample. Previous experiments have shown irregularities in the level degeneracy and should be reconsidered in this context.
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