We study numerically the nature of biexcitons in semiconducting single-walled carbon nanotubes by exactly solving the two-electron-two-hole problem in the realistic Hamiltonian derived using the k·p and screened Hartree-Fock approximation. Our treatment captures the essential features of narrow-gap semiconductors, i.e., band nonparabolicity, form factors in the density operators, and many-body effects. It turns out that the form factor as well as the screening effect significantly suppresses the biexciton binding energy. The Haynes factor we obtained by including all the above features is less than half the values predicted in the phenomenological model. We expect them to be the general aspects observed in narrow-gap semiconductor systems.
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