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 (V-0) and extended (V-1/r) 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 (alpha,beta) space where alpha=V-1/V-0 and beta=t/V-0. The phase space generally supports multiple biexcitons; the most tightly bound biexciton exists over a region limited by beta less than or similar to 0.11 and 0.84 less than or similar to alpha 1. Higher-energy biexcitons occupy successively smaller corners of phase space centered on beta=0 and alpha=1. The two-photon absorption spectrum in the region 2h omega<2 Delta, where ii 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.