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

References in corpus (3)

• The electronic properties of graphene
• Chiral tunneling and the Klein paradox in graphene
• An Egorov Theorem for avoided crossings of eigenvalue surfaces

Cited by in corpus (4)

• Wavepackets in inhomogeneous periodic media: propagation through a one-dimensional band crossing
• An Egorov Theorem for avoided crossings of eigenvalue surfaces
• Coherent electronic transport in periodic crystals
• A New Cumulant Expansion Based Extraction for Higher Order Quantum Corrections in Equilibrium Wigner-Boltzmann Equation