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

JOURNAL OF COMPUTATIONAL PHYSICS

卷:327

Article

Kammerer, Clotilde Fermanian^1,2  Mehats, Florian^3,4 

[1] Univ Paris Est, Lab Anal & Math Appl, 61 Ave Gen Gaulle, F-94010 Creteil, France

[2] CNRS, 61 Ave Gen Gaulle, F-94010 Creteil, France

[3] Univ Rennes 1, IPSO Inria Team, Inst Rech Math Rennes, Campus Beaulieu, F-35042 Rennes, France

[4] CNRS, Campus Beaulieu, F-35042 Rennes, France

关键词: Dirac equation;    Graphene;    Kinetic equations;    Conical intersection;    Landau-Zener formula;   

DOI  :  10.1016/j.jcp.2016.09.010

来源: Elsevier

【 摘 要 】

In this article, we propose a new numerical scheme for the computation of the transport of electrons in a graphene device. The underlying quantum model for graphene is a massless Dirac equation, whose eigenvalues display a conical singularity responsible for non-adiabatic transitions between the two modes. We first derive a kinetic model which takes the form of two Boltzmann equations coupled by a collision operator modeling the non-adiabatic 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. We give analytic justification of the model and propose a series of numerical experiments studying the influences of the various sources of errors between the quantum and the kinetic models. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free