Zero modes of various graphene configurations from the index theorem

J. K. Pachos, A. Hatzinikitas, M. Stone

Research output: Contribution to journalArticlepeer-review


In this article we consider a graphene sheet that is folded in various compact geometries with arbitrary topology described by a certain genus, g. While the Hamiltonian of these systems is defined on a lattice one can take the continuous limit. The obtained Dirac-like Hamiltonian describes well the low energy modes of the initial system. Starting from first principles we derive an index theorem that corresponds to this Hamiltonian. This theorem relates the zero energy modes of the graphene sheet with the topology of the compact lattice. For g = 0 and g = 1 these results coincide with the analytical and numerical studies performed for fullerene molecules and carbon nanotubes while for higher values of g they give predictions for more complicated molecules.

Original languageEnglish (US)
Pages (from-to)127-132
Number of pages6
JournalEuropean Physical Journal: Special Topics
Issue number1
StatePublished - Sep 2007

ASJC Scopus subject areas

  • General Materials Science
  • General Physics and Astronomy
  • Physical and Theoretical Chemistry


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