Can Electric Field Induced Energy Gaps In Metallic Carbon Nanotubes?

The low-energy electronic structure of metallic single-walled carbon nanotube (SWNT) in an external electric field perpendicular to the tube axis is investigated. Based on tight-binding approximation, a field-induced energy gap is found in all (n, n) SWNTs, and the gap shows strong dependence on the electric field and the size of the tubes. We numerically find a universal scaling that the gap is a function of the electric field and the radius of SWNTs, and the results are testified by the second-order perturbation theory in weak field limit. Our calculation shows the field required to induce a 0.1 ${\rm eV}$ gap in metallic SWNTs can be easily reached under the current experimental conditions. It indicates a kind of possibility to apply nanotubes to electric signal-controlled nanoscale switching devices.