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

Abstract

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 þ 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 ! 1 of the second-order differential equation of an oscillator-type with a complex frequency satisfying some initial conditions at t ! À1. 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.

Asymptotic expansion of pair production probability in a time-dependent electric field

“…This distribution coincides with that of preceding studies re-expressed by the kinetic momentum [3,14,16]. Furthermore, the same expression is found in Ref.…”

“…This fact complicates the interpretation of the obtained results. In fact, in a preceding study, the canonical momentum is confused with the momentum a particle possesses because of its motion [14]. Moreover in our view, the discrepancy of the two momenta leads not only to inappropriate interpretation, but also to the incorrect result that the momentum spectra produced by a pulsed electric field and a constant electric field coincide when we take a limit of an infinite-time interval [3,15].…”

“…This is called the dynamically assisted Schwinger mechanism with which particle creation can be observed in the electric field below the critical strength [9][10][11]. Furthermore, it is indicated that the Schwinger mechanism is testable indirectly in the condensed matter system of a graphene single monolayer [12][13][14], in which the electrons inside are described approximately by the massless pseudo-relativistic Dirac equation.…”

Particle creation by peak electric field

“…Switch-ing the peak field on and off, we can imitate electric fields that are specific to condensed matter physics, in particular to graphene or Weyl semimetals as was reported, e.g., in Refs. [31][32][33][34][35][36][37][38][39].…”

Quantum field theory of the Casimir force for graphene

“…37 The same measurement data were compared 33 with the alternative theoretical predictions obtained in the framework of the hydrodynamic model of graphene. 6,7,39 It was shown 33 that the hydrodynamic model is excluded by the measurement data at a 99% confidence level over the wide region of separations. Thus, the experiment of Ref.…”