Biexciton on a one-dimensional lattice

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Abstract
The biexciton (excitonic molecule) is theoretically studied in a one-dimensional (1D) tight-binding model having both long-range Coulomb interactions and on-site interactions. We solve the four-fermion problem by the numerical diagonalization method for finite systems. The effect of particle correlation over the lattice-constant length scale is shown to be essential, which makes both of the conventional variational or Heitler-London approximations and the continuum models inadequate. In the phase diagram for the biexciton state, a crossover in the response to an increase in the long-range interaction is found to emerge, and occurs concomitantly with the Frenkel-Wannier crossover for single excitons. The dependence of the biexciton binding energy on the electron-hole mass ratio is also found for varying strength of the Coulomb interaction, where the behavior drastically differs from those in 2D or 3D continuum models. Two-photon absorption spectra are also obtained.