  The two-dimensional Dirac operator describes low-energy excitations in
graphene. Different choices for the boundary conditions give rise to
qualitative differences in the spectrum of the resulting operator. For a family
of boundary conditions, we find a lower bound to the spectral gap around zero,
proportional to $|\Omega|^{-1/2}$, where $\Omega \subset \mathbb{R}^2$ is the
bounded region where the Dirac operator acts. This family contains the
so-called infinite mass and armchair cases used in the physics literature for
the description of graphene quantum dots.
