  We introduce two simple models to study the effect of a spatially localized
transverse electric field on the low-energy electronic structure of
semiconducting carbon nanotubes. Starting from the Dirac Hamiltonian for the
low energy states of a carbon nanotube, we use scattering theory to show that
an arbitrarily weak field leads to the formation of localized electronic states
inside the free nanotube band gap. We study the binding energy of these subgap
states as a function of the range and strength of the electrostatic potential.
When the range of the potential is held constant and the strength is varied,
the binding energy shows crossover behavior: the states lie close to the free
nanotube band edge until the potential exceeds a threshold value, after which
the binding energy increases rapidly. When the potential strength is held
constant and the range is varied, we find resonant behavior: the binding energy
passes through a maximum as the range of the potential is increased. Large
electric fields confined to a small region of the nanotube are required to
create localized states far from the band edge.
