Bandgap modulation of narrow-gap carbon nanotubes in a transverse electric field

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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 π- and σ-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.