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

TL;DR

This paper explores quantum electrodynamics with anisotropic scaling in bilayer graphene, analyzing the Heisenberg-Euler action and Schwinger pair production, revealing unique scaling laws due to quadratic fermion dispersion.

Contribution

It introduces a novel anisotropic QED framework applicable to bilayer graphene, extending the understanding of quantum field theory in anisotropic vacua.

Findings

Derived the Heisenberg-Euler action for anisotropic QED in bilayer graphene.

Analyzed Schwinger pair production under anisotropic scaling laws.

Identified distinct scaling behaviors of electric and magnetic fields in the system.

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 Heisenberg-Euler action and Schwinger pair production in such anisotropic QED