dorsal/arxiv
View SchemaZero modes of various graphene configurations from the index theorem
| Authors | Jiannis K. Pachos, Agapitos Hatzinikitas, Michael Stone |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0701203 |
| URL | https://arxiv.org/abs/quant-ph/0701203 |
| DOI | 10.1140/epjst/e2007-00232-6 |
| Journal | Eur. Phys. J., Special Topics, 148, 127 (2007) |
Abstract
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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"abstract": "In this article we consider a graphene sheet that is folded in various\ncompact geometries with arbitrary topology described by a certain genus, $g$.\nWhile the Hamiltonian of these systems is defined on a lattice one can take the\ncontinuous limit. The obtained Dirac-like Hamiltonian describes well the low\nenergy modes of the initial system. Starting from first principles we derive an\nindex theorem that corresponds to this Hamiltonian. This theorem relates the\nzero energy modes of the graphene sheet with the topology of the compact\nlattice. For $g=0$ and $g=1$ these results coincide with the analytical and\nnumerical studies performed for fullerene molecules and carbon nanotubes while\nfor higher values of $g$ they give predictions for more complicated molecules.",
"arxiv_id": "quant-ph/0701203",
"authors": [
"Jiannis K. Pachos",
"Agapitos Hatzinikitas",
"Michael Stone"
],
"categories": [
"quant-ph"
],
"doi": "10.1140/epjst/e2007-00232-6",
"journal_ref": "Eur. Phys. J., Special Topics, 148, 127 (2007)",
"title": "Zero modes of various graphene configurations from the index theorem",
"url": "https://arxiv.org/abs/quant-ph/0701203"
},
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