  In this paper the two-dimensional Dirac operator with a general hermitian
$\delta$-shell interaction supported on a straight line is introduced as a
self-adjoint operator and its spectral properties are investigated in detail.
In particular, it is demonstrated that the singularly continuous spectrum is
always empty and that by switching a certain $\delta$-shell interaction on, it
is possible to generate an eigenvalue in the gap of the spectrum of the free
operator or to partially or even fully close the gap. This suggests that the
studied operators may serve as interesting continuum toy-models for Dirac
materials. Finally, approximations by Dirac operators with regular potentials
are presented.
