Approximate Solutions of a Kinetic Theory for Graphene

TL;DR

This paper analyzes an effective mass approximation within a nonperturbative kinetic theory framework for strong field excitations in graphene, showing its effectiveness under specific parameter conditions relevant for quantum radiation studies.

Contribution

It introduces a nonperturbative kinetic theory approach to approximate solutions in graphene's strong field excitations, expanding the analytical understanding of charge carrier dynamics.

Findings

Effective in a certain parameter range for electromagnetic pulses

Applicability condition:   < 1 for harmonic fields

Comparison with massive QED shows narrow usability of similar approximations

Abstract

The effective mass approximation is analysed in a nonperturbative kinetic theory approach to strong field excitations in graphene [1,2]. This problem is highly actual for the investigation of quantum radiation from graphene [3], where the collision integrals in the photon kinetic equation are rather complicated functionals of the distribution functions of the charge carriers. These functions are needed in the explicit analytical definition as solutions of the kinetic equations for the electron-hole excitations. In the present work it is shown that the suggested approach is rather effective in a certain range of parameters for the pulse of an external electromagnetic field. For example, the applicability condition of the approximation in the case of a harmonic field is $\hbar \omega^2 / (\sqrt{2} e E_0 v_F) < 1$, were $v_F$ is the Fermi velocity. In the standard massive quantum electrodynamics the usability of the analogical approximation is very narrow.