Zero modes of various graphene configurations from the index theorem
School of Physics and Astronomy, University of Leeds, Leeds, LS2 9JT, UK
2 School of Sciences, University of Aegean, 83200 Samos, Greece
3 Department of Physics, University of Illinois, 1110, W. Green St. Urbana, IL, 61801, USA
Corresponding author: firstname.lastname@example.org
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.
© EDP Sciences, Springer-Verlag, 2007