Singlet and triplet biexciton spectra of molecular crystals

The theory of the coherent pairing of Frenkel excitons in the presence of a resonant electromagnetic field is generalized to include the effect of the electron spin. It is shown that at high exciton densities and when the electromagnetic field is at resonance or near resonance, the removal of the spin degeneracy of the exciton pairs results in generating two fields, the singlet and the triplet biexciton fields, respectively. The gap functions ${\Delta }_{+}$ and ${\Delta }_{-}$ due to the singlet and triplet biexciton fields, respectively, are calculated and they are found to be independent of one another only in the limit when the exchange interactions between the charges disappear. In this limit, the energy modes for singlet and triplet biexciton fields have well-defined meaning and propagate through the crystal independently. A dielectric gap is induced by the electromagnetic field, which produces the energy splitting in the singlet biexciton spectrum, and it must be less than that of ${\Delta }_{+}$ for the singlet biexciton state. For finite values of the exchange interaction, the gap functions ${\Delta }_{+}$ and ${\Delta }_{-}$ depend strongly on each other and consequently the singlet and triplet biexciton fields are strongly mixed together. Optical transitions to the singlet and triplet biexciton states are considered and the corresponding expressions for the absorption coefficient are derived. The ground-state energy describing the binding energy arising from the singlet and triplet biexciton fields is calculated and discussed. Numerical estimates indicate that at high exciton densities, namely, for exciton concentrations ${10}^{18}$-${10}^{19}$ ${\mathrm{cm}}^{-3\mathrm{}}$ and when the ratio of the average exciton-exciton interaction over the average kinetic energy is between 0.7 and 2 (strong-coupling limit), the energy gap due to the singlet biexciton state is in the range 40-650 ${\mathrm{cm}}^{-1\mathrm{}}$, the corresponding transition temperature is 33-534 °K, while the binding energy is 22-684 ${\mathrm{cm}}^{-1\mathrm{}}$.