Theory of biexcitons in one-dimensional polymers

We calculate the biexciton phase space for a model polymer consisting of a one-dimensional array of N coupled quantum cells, each containing two levels. The Hamiltonian allows for electron and hole transfer (t) and includes on-site (V₀) and extended (V₁r) Coulombic interactions. The double electron-hole pair basis set is numerically diagonalized for as many as $N=31$ cells. A phase boundary for two-photon-allowed biexcitons with A⁺ symmetry is calculated in (α, β) space where α≡V₁V₀ and β≡tV₀. The phase space generally supports multiple biexcitons; the most tightly bound biexciton exists over a region limited by β0.11 and 0.84α<~1. Higher-energy biexcitons occupy successively smaller corners of phase space centered on β=0 and α=1. The two-photon absorption spectrum in the region 2ω<2Δ, where Δ is the one-photon gap, generally shows two types of peaks: high-energy ones associated with biexcitons and lower-energy peaks associated with single excitons of A⁺ symmetry.