Emerging Dirac and Majorana fermions for carbon nanotubes with proximity-induced pairing and spiral magnetic field

We study the low-energy band structure of armchair and small-band-gap 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 small-band-gap semiconducting tube with the field in the same plane, a nondegenerate zero mode at momentum k = 0 can be induced, allowing for the generation of topologically protected Majorana fermion end states.