An index Theorem for Graphene

Jiannis Pachos

DAMTP, University of Cambridge, U.K.

We analyze a graphene sheet folded in a compact geometry with arbitrary topology, including fullerene molecules and nanotube configurations. In the continuous limit, the Hamiltonian takes the form of the Dirac operator, which provides a good description of the low energy spectrum of the lattice system. By considering the Dirac operator we derive an index theorem that relates the zero modes of the Hamiltonian with the topology of the compact lattice. The result coincides with analytical and numerical studies for the known cases of fullerene molecules and carbon nanotubes.

Back