  We have considered non-magnetic materials with weak spin-orbit coupling, that
are periodic in two non-collinear directions, and finite in third, orthogonal
direction. In some cases, combined time-reversal and crystal symmetry of such
systems, allows the existence of Dirac cones at certain points in the
reciprocal space. We have investigated in a systematic way, all points of
Brillouin zone of all 80 diperiodic groups and have found sufficient conditions
for the existence of s=1/2 Dirac fermions, with symmetry-provided band touching
at the vertex of the Dirac cones. Conversely, complete linear dispersion is
forbidden for orbital wave-functions belonging to two-dimensional irreducible
representations (irreps) of little groups that do not satisfy certain
group-theoretical conditions given in this paper. Our results are illustrated
by a tight-binding example.
