The Schwinger mechanism and graphene

TL;DR

This paper derives the Schwinger pair production rate for 2+1 dimensional theories and suggests that graphene could be used to experimentally observe this quantum phenomenon.

Contribution

It provides a theoretical derivation of the Schwinger mechanism in 2+1 dimensions and proposes an experimental setup using graphene to test this effect.

Findings

Derived pair production rate formula for 2+1D systems

Proposed experimental configuration using graphene

Argued feasibility with current graphene samples

Abstract

The Schwinger mechanism, the production of charged particle-antiparticle pairs in a macroscopic external electric field, is derived for 2+1 dimensional theories. The rate of pair production per unit area for four species of massless fermions, with charge $q$, in a constant electric field $E$ is given by $ \pi^{-2} \hbar^{-3/2} \tilde{c}^{-1/2} (q E)^{3/2} $ where $\tilde{c}$ is the speed of light for the two-dimensional system. To the extent undoped graphene behaves like the quantum field-theoretic vacuum for massless fermions in 2+1 dimensions, the Schwinger mechanism should be testable experimentally. A possible experimental configuration for this is proposed. Effects due to deviations from this idealized picture of graphene are briefly considered. It is argued that with present day samples of graphene, tests of the Schwinger formula may be possible.