Degeneracy in carbon nanotubes under transverse magnetic δ-fields

The aim of this article was to study the degeneracy of the energy spectrum in a nanotube under a transverse magnetic field. The massless Dirac-Weyl equation has been used to describe the low energy states of this system. The particular case of a singular magnetic field approximated by Dirac delta distributions is considered. It is shown that, under general symmetry conditions, there is a double degeneracy corresponding to periodic solutions with null axial momentum k(z)=0. Also, there may be a kind of sporadic degeneracy for non-vanishing values of k(z), which are explicitly computed in the present example. The proof of these properties is obtained by means of the supersymmetric structure of the Dirac-Weyl Hamiltonian.