Infinite mass boundary conditions for Dirac operators

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