Electronic Structure of Single- and Multiple-shell Carbon Fullerenes

Abstract

We study the electronic states of giant single-shell and the recently discovered nested multi-shell carbon fullerenes within the tight-binding approximation. We use two different approaches, one based on iterations and the other on symmetry, to obtain the $\pi$-state energy spectra of large fullerene cages: $C_{240}$, $C_{540}$, $C_{960}$, $C_{1500}$, $C_{2160}$ and $C_{2940}$. Our iteration technique reduces the dimensionality of the problem by more than one order of magnitude (factors of $\sim 12$ and $20$), while the symmetry-based approach reduces it by a factor of $10$. We also find formulae for the highest occupied and lowest unoccupied molecular orbital (HOMO and LUMO) energies of $C_{60\cdot n^2}$ fullerenes as a function of $n$, demonstrating a tendency towards metallic regime for increasing $n$. For multi-shell fullerenes, we analytically obtain the eigenvalues of the intershell interaction.

5 pages, RevTex, 2 figures upon request (to be published in Physical Review B, Feb. 1994)

References in corpus (1)

• Electronic interactions in fullerene spheres

Cited by in corpus (4)

• Electronic polarizability as the fundamental variable in the dielectric properties of two-dimensional materials
• The continuum gauge field-theory model for low-energy electronic states of icosahedral fullerenes
• Low energy electronic states in spheroidal fullerenes
• Recursion and Path-Integral Approaches to the Analytic Study of the Electronic Properties of $C_{60}$