  We study the low-energy bandstructure of armchair and small-bandgap
semiconducting carbon nanotubes with proximity-induced superconducting pairing
when a spiral magnetic field creates strong effective spin-orbit interactions
from the Zeeman term and a periodic potential from the orbital part. We find
that gapless Dirac fermions can be generated by variation of a single
parameter. For a semiconducting tube with the field in the same plane, a
non-degenerate zero mode at momentum k=0 can be induced, allowing for the
generation of topologically protected Majorana fermion end states.
