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We report that symmetry breaking by a magnetic field can drastically increase the photoluminescence quantum yield of single-walled carbon nanotubes, by as much as a factor of 6, at low temperatures. To explain this we have developed a theoretical model based on field-dependent exciton band structure and the interplay of Coulomb interactions and the Aharonov-Bohm effect. This conclusively explains our data as the first experimental observation of dark excitons 5-10 meV below the bright excitons.
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