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Preprints, Working Papers, ... Year : 2015

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

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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Dates and versions

hal-01160791 , version 1 (08-06-2015)
hal-01160791 , version 2 (09-06-2015)
hal-01160791 , version 3 (27-09-2017)

Identifiers

  • HAL Id : hal-01160791 , version 3

Cite

Clotilde Fermanian Kammerer, Florian Méhats. A kinetic model for the transport of electrons in a graphen layer. 2015. ⟨hal-01160791v3⟩
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