Quantum Size Effects in the Polarizability of Carbon Fullerenes

We investigate the size-dependent dielectric response of carbon fullerenes with up to $3840$ atoms in the framework of the linear response theory. Our results suggest a significant polarizability enhancement due to quantum size effects with respect to classical or semiclassical calculations. The accuracy of our results, based on a parametrized Hamiltonian, is verified by ab initio time dependent density functional calculations for smaller fullerenes. Our findings underline the importance of quantum effects in the electronic response of nano- and mesoscopic systems.

Figure 1

Atomic structure of four representative fullerene cages considered in this Letter, optimized in Ref. 17 using the LCAO functional of Ref. 18. Since the scale in the subfigures is not the same, we also provide, in parentheses, the average radii of the cages.

Figure 2

The size dependence of the polarizability enhancement factor ${\alpha }_{\mathrm{LCAO}}/{\alpha }_{\mathrm{Penn}}$, shown by the data points. ${\alpha }_{\mathrm{LCAO}}$ is the static polarizability, computed at the LR-LCAO level, and ${\alpha }_{\mathrm{Penn}}$ the semiclassical value of the polarizability based on Penn’s model. The dotted line is a guide to the eye. For small cages, the static polarizability enhancement first increases with an increasing number of atoms. After reaching the maximum value at ${\mathrm{C}}_{960}$, the static polarizability enhancement decreases monotonically. Still, for fullerenes as large as ${\mathrm{C}}_{3840}$, the value of the quantum polarizability exceeds the semiclassical value by $\approx 70\%$.