The European Physical Journal Special Topics

, Volume 148, Issue 1, pp 127–132 | Cite as

Zero modes of various graphene configurations from the index theorem

  • J. K. PachosEmail author
  • A. Hatzinikitas
  • M. Stone


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.


Fullerene Graphene Sheet European Physical Journal Special Topic Dirac Operator Zero Mode 
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Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Authors and Affiliations

  1. 1.School of Physics and Astronomy, University of LeedsLeedsUK
  2. 2.School of Sciences, University of AegeanSamosGreece
  3. 3.Department of PhysicsUniversity of IllinoisW. Green St. UrbanaUSA

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