Selection rules and linear absorption spectra of carbon nanotubes in axial magnetic fields

We derive a transparent and easy-to-use analytic expression for the selection rules and the optical dipole matrix elements for carbon nanotubes of arbitrary chirality in the presence of axial magnetic fields using a single-orbital π-electron tight-binding model. From this, we calculate the linear absorption spectrum for arbitrary polarization directions of the incident light, providing insight into all optically allowed transition. We show that the transverse absorption peaks can be selectively excited with circularly polarized light and spectrally resolved in an axial magnetic field.