Coulomb interaction effects on nonlinear optical response in C60, C70, and higher fullerenes

TL;DR

This study theoretically investigates the nonlinear optical responses of C60 and higher fullerenes, revealing that Coulomb interactions significantly influence their third-order susceptibilities, which increase with larger carbon numbers and smaller optical gaps.

Contribution

It provides a detailed theoretical analysis of Coulomb interaction effects on nonlinear optical properties of fullerenes, extending understanding beyond C60 to higher fullerenes.

Findings

Higher fullerenes exhibit larger third-order susceptibilities than C60.

Nonlinearity increases as the optical gap decreases in higher fullerenes.

Nonlinearity scales approximately with the fourth power of the carbon number under certain Coulomb interaction conditions.

Abstract

Nonlinear optical properties in the fullerene C$_{60}$ and the extracted higher fullerenes -- C$_{70}$, C$_{76}$, C$_{78}$, and C$_{84}$ -- 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 C$_{60}$. 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 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.