The Electronic Spectrum of Fullerenes from the Dirac Equation

TL;DR

This paper models the electronic spectrum of fullerenes using a Dirac equation framework, incorporating effects of curvature and gauge fields to describe molecules like C60.

Contribution

It introduces a continuum Dirac equation approach for fullerenes, accounting for curvature and gauge fields, advancing theoretical understanding of their electronic properties.

Findings

Dirac equation effectively describes flat graphite lattice.

Curvature effects modeled by gauge fields in the Dirac framework.

C60 molecules well represented by Dirac equation on a spherical surface.

Abstract

The electronic spectrum of sheets of graphite (plane honeycomb lattice) folded into regular polihedra is studied. A continuum limit valid for sufficiently large molecules and based on a tight binding approximation is derived. It is found that a Dirac equation describes the flat graphite lattice. Curving the lattice by insertion of odd numbered rings can be mimicked by coupling effective gauge fields. In particular the $C_{60}$ and related molecules are well described by the Dirac equation on the surface of a sphere coupled to a color monopole sitting at its center.