  Often a modification of microscopic symmetry in a system can result in a
dramatic change in its macroscopic properties. Here we report that symmetry
breaking by a tube-threading magnetic field can drastically increase the
photoluminescence quantum yield of semiconducting single-walled carbon
nanotubes, by as much as a factor of six, at low temperatures. To explain this
striking connection between seemingly unrelated properties, we have developed a
comprehensive theoretical model based on magnetic-field-dependent
one-dimensional exciton band structure and the interplay of strong 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 in single-walled carbon nanotubes. We predict that this quantum
yield increase can be made much larger in disorder-free samples.
