Abstract
On the basis of the well-known kinetic description of e − e + vacuum pair creation in strong electromagnetic fields in D = 3 + 1 QED we construct a nonperturbative kinetic approach to electron-hole excitations in graphene under the action of strong, time-dependent electric fields. We start from the simplest model of low-energy excitations around the Dirac points in the Brillouin zone. The corresponding kinetic equations are analyzed by nonperturbative analytical and numerical methods that allow to avoid difficulties characteristic for the perturbation theory. We consider different models for external fields acting in both, one and two dimensions. In the latter case we discuss the nonlinear interaction of the orthogonal currents in graphene which plays the role of an active nonlinear medium. In particular, this allows to govern the current in one direction by means of the electric field acting in the orthogonal direction. Investigating the polarization current we detected the existence of high frequency damped oscillations in a constant external electric field. When the electric field is abruptly turned off residual inertial oscillations of the polarization current are obtained. Further nonlinear effects are discussed.
Highlights
In recent years considerable interest has developed in a nonperturbative, dynamical description of transport phenomena in condensed matter physics inspired by the physics of strong electromagnetic fields [1]
We have obtained on a nonperturbative basis the kinetic equation (KE) for describing electron-hole excitations in graphene under the action of a spatially homogeneous time dependent electric field
The derivation of the KE is based on the transition to the quasiparticle representation [6]
Summary
In recent years considerable interest has developed in a nonperturbative, dynamical description of transport phenomena in condensed matter physics inspired by the physics of strong electromagnetic fields [1]. Particular attention was devoted to graphene (see, e.g., [2,3]) In this case there is an obvious similarity with the dynamical Schwinger effect in QED, the creation of electron-positron pairs from the vacuum in strong electromagnetic fields [4,5,6]. Such an adaptation is performed in the present work The application of these methods allows for advancement to nonperturbative investigations of nonlinear effects in graphene in the presence of strong external electric fields. The evolution of the order parameter is defined by the entire prehistory of the graphene evolution during the application of the external field This effect becomes apparent in the damped oscillations of the residual polarization current on the background of a constant residual conduction current (Section 4). We define a set of scale factors for the physical quantities time (t0), momentum (p0), and field strength (E0) according to t0
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