Helicity and broken symmetry of DNA-nanotube hybrids

We study breaking of the "supersymmetry" of an intrinsically achiral armchair carbon nanotube by means of a helical perturbation. Lowering of the symmetry results in the appearance of a non-zero effective mass for nanotube low-energy excitations, which otherwise are massless Dirac fermions. Other important consequences of the symmetry breaking are opening of gaps in the energy spectrum and shifting of the Fermi points, which we classify according to their functional dependence on the nanotube and helix parameters. Within each class the gaps are proportional to the inverse of the nanotube radius, and appear to be sensitive to the exact position of the helix in a unit cell. These results are of immediate importance for the study of DNA-nanotube complexes, and can be verified by means of optical/electron spectroscopy or tunneling microscopy.