JETP Letters

, Volume 95, Issue 8, pp 411–415 | Cite as

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

  • M. I. Katsnelson
  • G. E. Volovik
Condensed Matter


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.


JETP Letter Quantum Electrodynamic Dirac Point Single Layer Graphene Bilayer Graphene 
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Copyright information

© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  1. 1.Institute for Molecules and MaterialsRadboud University NijmegenNijmegenThe Netherlands
  2. 2.Low Temperature LaboratoryAalto University, School of Science and TechnologyAALTOFinland
  3. 3.Landau Institute for Theoretical PhysicsRussian Academy of SciencesMoscowRussia

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