An index theorem for graphene

Jiannis K. Pachos, Michael Stone

Research output: Contribution to journalArticlepeer-review


We consider a graphene sheet folded in an arbitrary geometry, compact or with nanotube-like open boundaries. 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. We derive an index theorem that relates the zero energy modes of the graphene sheet with the topology of the lattice. The result coincides with analytical and numerical studies for the known cases of fullerene molecules and carbon nanotubes, and it extends to more complicated molecules. Potential applications to topological quantum computation are discussed.

Original languageEnglish (US)
Pages (from-to)5113-5120
Number of pages8
JournalInternational Journal of Modern Physics B
Issue number30
StatePublished - Dec 10 2007


  • Graphene
  • Index theorem
  • Topological degeneracy

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Condensed Matter Physics


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