Carbon Nanotubes in Helically Modulated Potentials

TL;DR

This paper investigates how a helical potential influences the electronic properties of carbon nanotubes, revealing potential modifications to band gaps and Fermi velocity, with implications for DNA-CNT interactions.

Contribution

It provides a theoretical analysis of the effects of helically symmetric potentials on carbon nanotubes' electronic spectra, including conditions for gap reduction and velocity changes.

Findings

Minimum band gap of semiconducting nanotubes is reduced by weak helical potentials.

Fermi velocity in metallic nanotubes decreases under the potential.

Strong fields induce small gaps at the Fermi surface.

Abstract

We calculate effects of an applied helically symmetric potential on the low energy electronic spectrum of a carbon nanotube in the continuum approximation. The spectrum depends on the strength of this potential and on a dimensionless geometrical parameter, P, which is the ratio of the circumference of the nanotube to the pitch of the helix. We find that the minimum band gap of a semiconducting nanotube is reduced by an arbitrarily weak helical potential, and for a given field strength there is an optimal P which produces the biggest change in the band gap. For metallic nanotubes the Fermi velocity is reduced by this potential and for strong fields two small gaps appear at the Fermi surface in addition to the gapless Dirac point. A simple model is developed to estimate the magnitude of the field strength and its effect on DNA-CNT complexes in an aqueous solution. We find that under typical experimental conditions the predicted effects of a helical potential are likely to be small and we discuss several methods for increasing the size of these effects.