Section: New Results

Analysis of models for quantum transport of electrons in graphene layers

In [28] , two mathematical models for the self consistent quantum transport of electrons in a graphene layer are presented are analyzed. We treat two situations. First, when the particles can move in all the plane $R^2$, the model takes the form of a system of massless Dirac equations coupled together by a selfconsistent potential, which is the trace in the plane of the graphene of the 3D Poisson potential associated to surface densities. Second, we consider a situation where the particles are constrained in a regular bounded domain $\Omega$. In order to take into account Dirichlet boundary conditions which are not compatible with the Dirac Hamiltonian $H_0$, we propose a different model built on a modified Hamiltonian displaying the same energy band diagram as $H_0$ near the Dirac points.