The Schwinger mechanism and graphene

Understand

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.