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 ($\frac{V_1}{r}$) Coulombic interactions. The double electron-hole pair basis set is numerically diagonalized for as many as $N=31\mathrm{}$ cells. A phase boundary for two-photon-allowed biexcitons with $A^{+}$ symmetry is calculated in ($\alpha$, $\beta$) space where $\alpha \equiv \frac{V_1}{V_0}$ and $\beta \equiv \frac{t}{V_0}$. The phase space generally supports multiple biexcitons; the most tightly bound biexciton exists over a region limited by $\beta \lesssim 0.11$ and $0.84\lesssim \alpha <~1$. Higher-energy biexcitons occupy successively smaller corners of phase space centered on $\beta =0\mathrm{}$ and $\alpha =1\mathrm{}$. The two-photon absorption spectrum in the region $2\hslash \omega <2\mathrm{}\Delta$, where $\Delta$ 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.