Carbon Nanotubes in Helically Modulated Potentials

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-carbon nanotube 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. Disciplines Physical Sciences and Mathematics | Physics Comments Suggested Citation: P.J. Michalski and E.J. Mele. (2008). "Carbon nanotubes in helically modulated potentials." Physical Review B. 77, 085429. © 2008 The American Physical Society http://dx.doi.org/10.1103/PhysRevB.77.085429 This journal article is available at ScholarlyCommons: http://repository.upenn.edu/physics_papers/104 Carbon nanotubes in helically modulated potentials P. J. Michalski and E. J. Mele Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA Received 30 August 2007; revised manuscript received 3 December 2007; published 27 February 2008 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-carbon nanotube 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. DOI: 10.1103/PhysRevB.77.085429 PACS number s : 73.22.Dj, 73.43.Cd, 73.63.Fg