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

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• 作者：Clotilde Fermanian Kammerer^a ; ^{Clotilde.Fermanian@u-pec.fr" class="auth_mail" title="E-mail the corresponding author} ; Florian Mé ; hats^b ; ^{florian.mehats@univ-rennes1.fr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Dirac equation ; Graphene ; Kinetic equations ; Conical intersection ; Landau&ndash ; Zener formula
• 刊名：Journal of Computational Physics
• 出版年：2016
• 出版时间：15 December 2016
• 年：2016
• 卷：327
• 期：Complete
• 页码：450-483
• 全文大小：1308 K

文摘

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.