Infinite mass boundary conditions for Dirac operators

Abstract

We study a self-adjoint realization of a massless Dirac operator on a bounded connected domain $\Omega \subset {\mathbb{R}}^2$ which is frequently used to model graphene. In particular, we show that this operator is the limit, as $M\to \infty$, of a Dirac operator defined on the whole plane, with a mass term of size $M$ supported outside $\Omega$.