Hanne van den Bosch

Dirac operators describing Graphene Quantum Dots

Low energy electronic excitations in graphene, a two-dimensional lattice of carbon atoms, are described effectively by a two–dimensional Dirac operator. For a bounded flake of graphene (a quantum dot), the choice of boundary conditions determines various properties of the spectrum. Several of these choices appear in the physics literature on graphene. For a simply connected flake and a family of boundary conditions, we obtain an explicit lower bound on the spectral gap around zero.
This is joint work with Rafael Benguria, Edgardo Stockmeyer (PUC, Chile), Søren Fournais (Aarhus) and Cristóbal Vallejos (Penn State).