High field magneto-optical spectroscopy of highly aligned individual and ensemble single-walled carbon nanotubes

The tubular nature of single-walled carbon nanotube (SWCNT) crystals allows them to exhibit non-intuitive quantum phenomena when threaded by a magnetic flux, which breaks the time reversal symmetry and adds an Aharonov-Bohm phase to the circumferential boundary conditions on the electronic wave function. We demonstrate that such a symmetry-breaking magnetic field can dramatically "brighten" an optically-inactive, or dark, exciton state at low temperature. 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. Most recently, we made the direct observation of the dark excitonic state in individual SWCNTs using low-temperature micro-photoluminescence (PL) and and verified the importance of a parallel, tube-threading magentic field with ensemble spectroscopy. For micro-PL, a magnetic field up to 5 T, applied along the nanotube axis, brightened the dark state, leading to the emergence of a new emission peak. The peak rapidly grew in intensity with increasing field at the expense of the originally-dominant bright exciton peak and finally became dominant at fields > 3 T. The directly measured dark-bright splitting values were 1-4 meV for tube diameters 1.0-1.3 nm. For ensemble PL, we used fields up to 55 T in two collection geometries to demonstrate the importance of the tube-threading component. These experiments have provided one of the most critical tests for recently-proposed theories of 1-D excitons taking into account the strong 1-D Coulomb interactions and unique band structure on an equal footing.