Temperature-dependent magneto-photoluminescence spectroscopy of carbon nanotubes: evidence for dark excitons

We review recent experimental and theoretical studies on the radiative properties of excitons in single-walled carbon nanotubes (SWNTs) as a function of magnetic field and temperature. These studies not only provide new insight into the fundamental properties of excitons in the ultimate one-dimensional (1D) limit but also reveal new phenomena associated with the unique crystal and electronic structure of SWNTs.During the past several years, SWNTs have emerged as one of the most ideal systems available for the systematic study of ID excitons, which are predicted to possess a set of properties that are distinctly different from excitons in higher dimensions. In addition, their tubular nature allows them to exhibit non-intuitive quantum phenomena when subjected to a parallel magnetic field, which breaks time reversal symmetry and adds an Aharonov-Bohm phase to the electronic wave-function. In particular, a series of recent experiments demonstrate that such a symmetry-breaking magnetic field can dramatically brighten an optically-inactive, or dark, exciton state at low temperature (see the title figure on the right). We show that this phenomenon, magnetic brightening, can be understood as a consequence of interplay between the strong intervalley Coulomb mixing and field-induced lifting of valley degeneracy. Detailed temperature-dependent photoluminescence studies of excitons in SWNTs in a varying magnetic field have thus provided one of the most critical tests for recently proposed theories of 1D excitons taking into account the strong 1D Coulomb interactions and unique band structure on an equal footing. Furthermore, results of these studies suggest the intriguing possibility of manipulating the optical properties of SWNTs by judicious symmetry control, which can lead to novel devices and applications in lasers and optoelectronics.