The formalism of the nonperturbative description of transport phenomena in graphene on the framework of the quantum kinetic equation for the Schwinger-like process is compared with the description on the basis of Zener-Klein tunneling. The regime of ballistic conductivity in a constant electric field is considered. In the latter case the interaction of carriers with electric field is described in terms of the spatial dependence of their potential energy (x-representation). The presented kinetic formalism uses an alternative method of describing the interaction with a field through the introduction of a quasimomentum $P=p-(e/c)A(t)$ where $A(t)$ is the vector potential (t-representation). Both approaches should lead to the same physical characteristics of the described process. The measurement of the current in experiments is realized in static conditions determined by the potential difference between the electrodes and the distance between them. These parameters are native for the x-representation. On the contrary, in the approach based on the t-representation it is necessary to consider the situation in dynamics and introduce the effective lifetime of the generated carriers. In the ballistic regime this time depends on the distance between the electrodes. We give a detailed comparison of these two descriptions of the current and demonstrate good coincidence with the experimental data of the alternative approach based on the t-representation. It provides a reliable foundation for the application of nonperturbative methods adopted from strong field QED, that allows to include in the consideration more general models of the field (arbitrary polarization and time dependence) and to extend the scope of the theory.
Published : "arXiv Mesoscale and Nanoscale Physics".