Antiferromagnetic Dirac semimetals in two dimensions

The search for symmetry-protected two-dimensional (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 belong to a 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.