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Two-dimensional gas of massless Dirac fermions in graphene

Nature volume 438, pages 197200 (10 November 2005) | Download Citation



Quantum electrodynamics (resulting from the merger of quantum mechanics and relativity theory) has provided a clear understanding of phenomena ranging from particle physics to cosmology and from astrophysics to quantum chemistry1,2,3. The ideas underlying quantum electrodynamics also influence the theory of condensed matter4,5, but quantum relativistic effects are usually minute in the known experimental systems that can be described accurately by the non-relativistic Schrödinger equation. Here we report an experimental study of a condensed-matter system (graphene, a single atomic layer of carbon6,7) in which electron transport is essentially governed by Dirac's (relativistic) equation. The charge carriers in graphene mimic relativistic particles with zero rest mass and have an effective ‘speed of light’ c* ≈ 106 m s-1. Our study reveals a variety of unusual phenomena that are characteristic of two-dimensional Dirac fermions. In particular we have observed the following: first, graphene's conductivity never falls below a minimum value corresponding to the quantum unit of conductance, even when concentrations of charge carriers tend to zero; second, the integer quantum Hall effect in graphene is anomalous in that it occurs at half-integer filling factors; and third, the cyclotron mass mc of massless carriers in graphene is described by E = mcc*2. This two-dimensional system is not only interesting in itself but also allows access to the subtle and rich physics of quantum electrodynamics in a bench-top experiment.

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We thank L. Glazman, V. Falko, S. Sharapov and A. Castro Neto for discussions. K.S.N. was supported by Leverhulme Trust. S.V.M., S.V.D. and A.A.F. acknowledge support from the Russian Academy of Science and INTAS. This research was funded by the EPSRC (UK).

Author information


  1. Manchester Centre for Mesoscience and Nanotechnology, University of Manchester, Manchester M13 9PL, UK

    • K. S. Novoselov
    • , A. K. Geim
    • , D. Jiang
    •  & I. V. Grigorieva
  2. Institute for Microelectronics Technology, 142432 Chernogolovka, Russia

    • S. V. Morozov
    • , S. V. Dubonos
    •  & A. A. Firsov
  3. Institute for Molecules and Materials, Radboud University of Nijmegen, Toernooiveld 1, 6525 ED Nijmegen, The Netherlands

    • M. I. Katsnelson


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Reprints and permissions information is available at npg.nature.com/reprintsandpermissions. The authors declare no competing financial interests.

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Correspondence to K. S. Novoselov or A. K. Geim.

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