Excitons inC60studied by temperature-dependent optical second-harmonic generation

The electric-dipole-forbidden ${}_{}{}^1{}_{}{}^{}$ ${\mathit{T}}_{1\mathit{g}}$ excitonic state of solid ${\mathrm{C}}_{60}$ at ħω=1.81 eV can be probed with a second-harmonic generation (SHG) experiment. We show that the SHG line shape depends strongly on the degree of rotational order. We observe a splitting into two peaks below the rotational ordering phase-transition temperature of 260 K. The origin of this splitting is discussed in terms of a possible Jahn-Teller effect, a possible Davydov splitting due to the four molecules per unit cell in the low-temperature phase, and a mixing of the nearly degenerate ${}_{}{}^1{}_{}{}^{}$ ${\mathit{T}}_{1\mathit{g}}$ and ${}_{}{}^1{}_{}{}^{}$ ${\mathit{G}}_{\mathit{g}}$ free molecule states because of the lower symmetry in the solid. The exciton band structure is calculated with a charge-transfer-mediated propagation mechanism as suggested by Lof et al. and with one-electron (-hole) transfer integrals determined from band-structure calculations. Comparison with our experimental SHG data leads to a reasonable agreement and shows that a mixing of ${}_{}{}^1{}_{}{}^{}\mathrm{\Gamma }_{1\mathit{g}}^{}{}_{}{}^{}$ and ${}_{}{}^1{}_{}{}^{}$ ${\mathit{G}}_{\mathit{g}}$ states may explain the splitting at low temperature.