Effects of Coulomb interaction on the nonlinear optical response in , and higher fullerenes

Nonlinear optical properties of the fullerene and extracted higher fullerenes - , and - are theoretically investigated by using the exciton formalism and the sum-over-states method. We find that the off-resonant third-order susceptibilities of higher fullerenes are a few times larger than those of . The magnitude of the nonlinearity increases as the optical gap decreases for higher fullerenes. The nonlinearity is nearly proportional to the fourth power of the carbon number when the on-site Coulomb repulsion is 2t or 4t, t being the nearest-neighbour hopping integral. This result, indicating important roles of Coulomb interactions, agrees with quantum chemical calculations for higher fullerenes.