Zero modes of various graphene configurations from the index theorem

Details Zero modes of various graphene configurations from the index theorem Zero modes of various graphene configurations from the index theorem

2007-01-28

arxiv.org/abs/quant-ph/0701203v1

Eur. Phys. J., Special Topics, 148, 127 (2007)

Physics

Quantum Physics

7 pages, 1 figure. Proceedings of the Graphene Conference, MPI PKS Dresden, September 2006

Scientific paper

10.1140/epjst/e2007-00232-6

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.

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