Band Gap in Graphene with Periodic Potentials
December 7 – 18, 2015

Recent experiments on graphene showed that producing periodic perforations in a graphene sample open a gap at the Fermi energy, turning the sample into a semi-conductor. The aim of this REB, is to derive a model for this semi-conductor, and prove the opening of a gap. The lack of a distinguished Friedrichs extension for a Dirac operator defined on R2\Ω, where Ω is an open subset of R2, renders the modelization of such problem much more difficult than in the Schrödinger case. For that sake, we shall study the 2 dimensional Dirac operator with a sclar mass term modelizing perforations, and prove that the spectrum near zero has a gap, whose size depends on the shape and strenght of this potential.


Jean-Marie Barbaroux (Université Sud Toulon-Var)
Horia Cornean (Aalborg University)
Edgardo Stockmeyer (
Pontificia Catolica University of Chile)