The momentum spectrum of positively and negatively charged carriers created in intrinsic graphene submitted to a time-dependent external electric field is evaluated for many external field configurations. Owing to the formal analogy between relativistic quantum mechanics and the description of graphene quasiparticles in terms of the massless Dirac equation, the electron momentum density is evaluated within two-dimensional massless quantum electrodynamics coupled to a strong classical field. This allows the treatment of dynamical effects in electron-hole creation and gives a physical description in terms of the time-dependent Schwinger mechanism. At zero transverse momentum, it is shown that the Fermi bound in the electron-hole momentum spectrum is saturated in a certain momentum window and the pair density depends only on the potential difference between asymptotic potentials before and after the interaction. The pair density for nonzero transverse momenta is evaluated using numerical calculations. The numerical results demonstrate that an important number of pairs can be created by an external field through both tunneling and multiphoton processes. It is argued that these features of the dynamical pair production may facilitate the detection of the Schwinger mechanism using graphene as a condensed matter analog to quantum electrodynamics.

The electron momentum density obtained from the Schwinger-like mechanism is evaluated for a graphene sample immersed in a homogeneous time-dependent electric field. Based on the analogy between graphene low-energy electrons and quantum electrodynamics (QED), numerical techniques borrowed from strong field QED are employed and compared to approximate analytical approaches. It is demonstrated that for some range of experimentally accessible parameters, the pair production proceeds by sequences of adiabatic evolutions followed by non-adiabatic Landau-Zener transitions, reminiscent of the Kibble-Zurek mechanism describing topological defect density in second order phase transitions. For some field configurations, this yields interference patterns in momentum space which are explained in terms of the adiabatic-impulse model and the Landau-Zener-St\"{u}ckelberg interferometry.Comment: 13 pages, 12 figure