  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.
