The electronic spectrum of fullerenes from the Dirac equation

Abstract

The electronic spectrum of sheets of graphite (plane honeycomb lattice) folded into regular polyhedra is studied. A continuum limit valid for sufficiently large molecules and based on the 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 C60 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.