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

作者：Kammerer Clotilde Fermanian^*; Mehats Florian

来源：Journal of Computational Physics, 2016, 327: 450-483.

DOI：10.1016/j.jcp.2016.09.010

• Dirac equation
• Graphene
• Kinetic equations
• Conical intersection
• Landau-Zener formula

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.

• 出版日期2016-12-15
• 单位INRIA