Abstract
Nonlinear optical properties in the fullerenes C60 and C70, and in the extracted higher fullerenes -- C76, C78, and C84 -- are theoretically investigated by using the exciton formalism and the sum-over-states method. We find that off-resonant third order susceptibilities of higher fullerenes are a few times larger than those of C60. The magnitude of nonlinearity increases as the optical gap decreases in higher fullerenes. The nonlinearity is nearly proportional to the fourth power of the carbon number when the onsite Coulomb repulsion U is 2t or 4t, t being the nearest neighbor hopping integral. This result, indicating important roles of Coulomb interactions, agrees with quantum chemical calculations of higher fullerenes.

Table
Coulomb interaction dependence of the power alpha,
where |chi^(3)| ~ AtimesN^alpha and N the carbon number.

Figure 1
The absolute value of the off-resonant susceptibility |chi^(3)| for C60 and seven isomers of higher fullerenes, plotted against the energy gap (shown in units of t). The squares, circles, and triangles represent results for U = 0t, 2t, and 4t, respectively. The left axis is in the logarithmic scale.

Figure 2
The absolute value of the off-resonant susceptibility |chi^(3)| for C60 and seven isomers of higher fullerenes, plotted against the carbon number N. The squares, circles, and triangles represent results for U = 0t, 2t, and 4t, respectively. The left and bottom axes are in the logarithmic scale. The solid lines are the results of the linear fitting in the logarithmic scale: |chi^(3)| ~ AtimesN^alpha.