Symmetry-induced nonequilibrium distributions of bright and dark exciton states in single carbon nanotubes

We investigated the magnetic and temperature dependence of the bright and dark exciton luminescence spectra in single carbon nanotubes. We found that the phonon-induced exciton scattering rate from the bright to the dark state is only one order of magnitude larger than the dark exciton recombination rate below 10 K at zero magnetic field. Our results indicate that excitons are nonequilibriumly distributed between the bright and dark states due to the different parities of the wave functions and that Aharonov-Bohm flux enhances the phonon-induced exciton scattering between these two states. Our nonequilibrium exciton distribution model can also explain the nonzero photoluminescence intensity at very low temperatures.