
VOLUME 95  ISSUE 8 
PAGE 457

Quantum electrodynamics with anisotropic scaling: HeisenbergEuler action and Schwinger pair production in the bilayer graphene

M. I. Katsnelson, G. E. Volovik^{+*}
Radboud University Nijmegen, Institute for Molecules and Materials, NL6525AJ Nijmegen, The Netherlands ^{+}Low Temperature Laboratory, Aalto University, School of Science and Technology, P.O. Box 15100, FI00076 AALTO, Finland ^{*}Landau Institute for Theoretical Physics RAS, 119334 Moscow, Russia

Abstract
We discuss quantum electrodynamics emerging in the vacua with
anisotropic scaling. Systems with anisotropic scaling were
suggested by Horava 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 HeisenbergEuler action and Schwinger pair production
in such anisotropic QED.


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