Addition Energies of Fullerenes and Nanotubes as Quantum Dots: The Role of Symmetry

TL;DR

This study uses density-functional theory to explore how symmetry influences addition energy oscillations in quantum dots made of fullerenes and nanotubes, revealing the impact of symmetry and defects on electronic properties.

Contribution

It demonstrates the connection between symmetry, degeneracy, and addition energy oscillations in carbon-based quantum dots, providing explanations for experimental observations.

Findings

Highly symmetric fullerenes exhibit large oscillation periods due to degeneracy.

Long nanotubes show fourfold oscillations in addition energy.

Defects reduce symmetry, changing oscillation behavior to even/odd patterns.

Abstract

Using density-functional theory calculations, we investigate the addition energy (AE) of quantum dots formed of fullerenes or closed single-wall carbon nanotubes. We focus on the connection between symmetry and oscillations in the AE spectrum. In the highly symmetric fullerenes the oscillation period is large because of the large level degeneracy and Hund's rule. For long nanotubes, the AE oscillation is fourfold. Adding defects destroys the spatial symmetry of the tubes, leaving only spin degeneracy; correspondingly, the fourfold behavior is destroyed, leaving an even/odd behavior which is quite robust. We use our symmetry results to explain recent experiments. [Phys. Rev. Lett. 91, 116803 (2003).]