  The search for symmetry-protected 2D Dirac semimetals analogous to graphene
is important both for fundamental and practical interest. The 2D Dirac cones
are protected by crystalline symmetries and magnetic ordering may destroy their
robustness. Here we propose a general framework to classify stable 2D Dirac
semimetals in spin-orbit coupled systems having the combined time-reversal and
inversion symmetries, and show the existence of the stable Dirac points in 2D
antiferromagnetic semimetals. Compared to 3D Dirac semimetals which fall into
two distinct classes, Dirac semimetals in 2D with combined time-reversal and
inversion symmetries belongs to single class which is closely related to the
nonsymmorphic space group symmetries. We further provide a concrete model in
antiferromagnetic semimetals which supports symmetry-protected 2D Dirac points.
The symmetry breaking in such systems leads to 2D chiral topological states
such as quantum anomalous Hall insulator and chiral topological superconductor
phases.
