Antiferromagnetic Dirac semimetals in two dimensions

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