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Zero modes of various graphene confiurations from the index theorem

Pachos, J.K., Hatzinikitas, A. and Stone, M. (2007) Zero modes of various graphene confiurations from the index theorem. European Physical Journal - Special Topics, 148 (1). pp. 127-132. ISSN 1951-6401

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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.

Item Type: Article
Copyright, Publisher and Additional Information: © 2007 EDP Sciences S A. This is an author produced version of a paper published in European Physical Journal-Special Topics. Uploaded in accordance with the publisher's self-archiving policy.
Academic Units: The University of Leeds > Faculty of Maths and Physical Sciences (Leeds) > School of Physics and Astronomy (Leeds)
Depositing User: Sherpa Assistant
Date Deposited: 06 Nov 2007 10:57
Last Modified: 08 Feb 2013 17:05
Published Version: http://dx.doi.org/10.1140/epjst/e2007-00232-6
Status: Published
Publisher: E D P Sciences S.A.
Refereed: Yes
Identification Number: 10.1140/epjst/e2007-00232-6
URI: http://eprints.whiterose.ac.uk/id/eprint/3454

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