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Correlation and dimensional effects of trions in carbon nanotubes

We study the binding energies of singlet trions, i.e. charged excitons, in carbon nanotubes. The problem is modeled, through the effective-mass model, as a three-particle complex on the surface of a cylinder, which we investigate using both one- and two-dimensional expansions of the wave function. The effects of dimensionality and correlation are studied in detail. We find that the Hartree-Fock approximation significantly underestimates the trion binding energy. Combined with band structures calculated using a non-orthogonal nearest neighbour tight binding model, the results from the cylinder model are used to compute physical binding energies for a wide selection of carbon nanotubes. In addition, the dependence on dielectric screening is examined. Our findings indicate that trions are detectable at room temperature in carbon nanotubes with radius below 8Å.