A kinetic model for the transport of electrons in a graphen layer

Clotilde Fermanian Kammerer (1) , Florian Méhats (2, 3)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
2 IPSO - Invariant Preserving SOlvers
3 IRMAR - Institut de Recherche Mathématique de Rennes

In this article, a kinetic model for the transport of electrons in graphene is derived with the tools of semiclassical analysis. The underlying quantum model is a massless Dirac equation, whose eigenvalues display a conical singularity responsible for non adiabatic transitions between the two modes. Our kinetic model takes the form of two Boltzmann equations coupled by a collision operator modeling these transitions. This collision term includes a Landau-Zener transfer term and a jump operator whose presence is essential in order to ensure a good energy conservation during the transitions. We propose an algorithmic realization of the semi-group solving the kinetic model, by a particle method. In the last section, a series of numerical experiments are given in order to study the influences of the various sources of errors between the quantum and the kinetic models.

Mots clés: graphen; kinetic equations; conical intersections

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]

Clotilde Fermanian Kammerer, Florian Méhats. A kinetic model for the transport of electrons in a graphen layer. 2015. ⟨hal-01160791v2⟩