Creation of quasiparticles in graphene by a time-dependent electric field

We investigate the creation of massless quasiparticle pairs from the vacuum state in graphene by the space homogeneous time-dependent electric field. For this purpose the formalism of ($2+1$)-dimensional quantum electrodynamics is applied to the case of a nonstationary background with arbitrary time dependence allowing the $S$-matrix formulation of the problem. The number of created pairs per unit of graphene area is expressed via the asymptotic solution at $t\ensuremath{\rightarrow}\ensuremath{\infty}$ of the second-order differential equation of an oscillator-type with a complex frequency satisfying some initial conditions at $t\ensuremath{\rightarrow}\ensuremath{-}\ensuremath{\infty}$. The obtained results are applied to the electric field with specific dependence on time admitting the exact solution of the Dirac equation. The number of created pairs per unit area is calculated analytically in a wide variety of different regimes depending on the parameters of the electric field. The investigated earlier case of the static electric field is reproduced as a particular case of our formalism. It is shown that the creation rate in a time-dependent field is often larger than in a static field.

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