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arXiv · 1605.02451

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

Clotilde Fermanian Kammerer·Florian Méhats
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Abstract

In this article, we propose a new numerical model for 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.

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Clotilde Fermanian Kammerer, Florian Méhats. 2016-05-09. A kinetic model for the transport of electrons in a graphene layer. https://doi.org/10.1016/j.jcp.2016.09.010

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