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Mesoscopics in Graphene: Dirac Points in Periodic Geometries

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Graphene Nanoelectronics

Part of the book series: NanoScience and Technology ((NANO))

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Abstract

We review the interesting physics associated with two possible realizations of mesoscopic graphene systems where periodicity plays an important role: graphene rings, and graphene in a superlattice potential. The electronic spectra of graphene rings contain signatures of “effective time reversal symmetry breaking,” which are naturally interpreted in terms of effective magnetic flux contained in the ring, even when no real flux is present. This remarkable behavior arises because the low energy physics of electrons is controlled by a Dirac equation. This also creates unusual effects in a one dimensional superlattice potential, which allows the number of Dirac points at zero energy to be manipulated by the strength and/or period of the potential. The emergence of new Dirac points is accompanied by strong signatures in the conduction properties of the system.

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Acknowledgements

The authors would like to thank many colleagues for collaborations and discussions related to this work. These include A.P. Iyengar, Tianhuan Luo, D. Arovas, and K. Ziegler. Funding for the work described here was provided by the MEC-Spain via Grant No. FIS2009-08744 (LB), and by the NSF through Grant No. DMR-0704033 (HAF).

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Authors and Affiliations

  1. Department of Physics, Indiana University, Bloomington, IN, 47401, USA

    H. A. Fertig

  2. Instituto de Ciencia de Materiales de Madrid (CSIC), Catoblanco, 28049, Madrid, Spain

    L. Brey

Authors
  1. H. A. Fertig
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  2. L. Brey
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Correspondence to H. A. Fertig .

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Editors and Affiliations

  1. , Electrical and Computer Engineering, University of Iowa, IATL 116, IOWA City, 52246, USA

    Hassan Raza

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© 2011 Springer-Verlag Berlin Heidelberg

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Fertig, H.A., Brey, L. (2011). Mesoscopics in Graphene: Dirac Points in Periodic Geometries. In: Raza, H. (eds) Graphene Nanoelectronics. NanoScience and Technology. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22984-8_10

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  • DOI: https://doi.org/10.1007/978-3-642-22984-8_10

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-20467-8

  • Online ISBN: 978-3-642-22984-8

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