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Quantum electrodynamics with anisotropic scaling: Heisenberg-Euler action and Schwinger pair production in the bilayer graphene

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Abstract

We discuss quantum electrodynamics emerging in the vacua with anisotropic scaling. Systems with anisotropic scaling were suggested by Hořava in relation to the quantum theory of gravity. In such vacua, the space and time are not equivalent, and moreover they obey different scaling laws, called the anisotropic scaling. Such anisotropic scaling takes place for fermions in bilayer graphene, where if one neglects the trigonal warping effects the massless Dirac fermions have quadratic dispersion. This results in the anisotropic quantum electrodynamics, in which electric and magnetic fields obey different scaling laws. Here we discuss the Heisenberg-Euler action and Schwinger pair production in such anisotropic QED.

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Authors and Affiliations

  1. Institute for Molecules and Materials, Radboud University Nijmegen, NL-6525AJ, Nijmegen, The Netherlands

    M. I. Katsnelson

  2. Low Temperature Laboratory, Aalto University, School of Science and Technology, P.O. Box 15100, FI-00076, AALTO, Finland

    G. E. Volovik

  3. Landau Institute for Theoretical Physics, Russian Academy of Sciences, Moscow, 119334, Russia

    G. E. Volovik

Authors
  1. M. I. Katsnelson
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  2. G. E. Volovik
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Correspondence to M. I. Katsnelson.

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Katsnelson, M.I., Volovik, G.E. Quantum electrodynamics with anisotropic scaling: Heisenberg-Euler action and Schwinger pair production in the bilayer graphene. Jetp Lett. 95, 411–415 (2012). https://doi.org/10.1134/S0021364012080061

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  • DOI: https://doi.org/10.1134/S0021364012080061

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