  Helical modes, conducting opposite spins in opposite directions, are shown to
exist in metallic armchair nanotubes in an all-electric setup. This is a
consequence of the interplay between spin-orbit interaction and strong electric
fields. The helical regime can also be obtained in chiral metallic nanotubes by
applying an additional magnetic field. In particular, it is possible to obtain
helical modes at one of the two Dirac points only, while the other one remains
gapped. Starting from a tight-binding model we derive the effective low-energy
Hamiltonian and the resulting spectrum.
