Bandgap modulation of narrow-gap carbon nanotubes in a transverse   electric field
  We propose a method to modulate the bandgaps in quasi-metallic carbon nanotubes using a transverse electric field. Unlike previous investigations, we include curvature effects of the nanotubes by incorporating both $\pi$- and $\sigma$-orbitals in our tight-binding calculations. The calculations show that the small curvature-induced bandgaps decrease quadratically with electric field amplitude to zero. As the electric field amplitude continues to increase, the bandgap then expands in a similar manner to that presented in earlier studies. The bandgap dependence is verified by analytical calculations, which also agree with preceding analyses for the limit of no curvature. 
D. Gunlycke, C. J. Lambert, S. W. D. Bailey, D. G. Pettifor, G. A. D.   Briggs, and J. H. Jefferson