The Schwinger mechanism and graphene

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 per unit time for four species of massless fermions, with charge e, in a constant electric field E is given by $ \pi^{-2} \hbar^{-3/2} \tilde{c}^{-1/2} \zeta ({3/2}) (e 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.