Size, Shape and Low Energy Electronic Structure of Carbon Nanotubes

TL;DR

This paper presents a theoretical model describing the low energy electronic structure of carbon nanotubes, accounting for size, shape, and symmetry effects, and provides analytical results for their electronic gap properties.

Contribution

It introduces a Dirac Hamiltonian approach on curved surfaces to analyze nanotube electronic properties, including effects of shape deformations and symmetry.

Findings

Analytical expressions for electronic gap structures in nanotubes

Effects of shape deformations on metallic nanotubes

Effective vector potential derived for curved nanotube surfaces

Abstract

A theory of the long wavelength low energy electronic structure of graphite-derived nanotubules is presented. The propagating $\pi$ electrons are described by wrapping a massless two dimensional Dirac Hamiltonian onto a curved surface. The effects of the tubule size, shape and symmetry are included through an effective vector potential which we derive for this model. The rich gap structure for all straight single wall cylindrical tubes is obtained analytically in this theory, and the effects of inhomogeneous shape deformations on nominally metallic armchair tubes are analyzed.