Projective Representations of Magnetic point groups and Dirac semimentals

In similar to the gapless Dirac fermions in particle physics, semimetals with Dirac-type point nodes also exist in condensed matter physics, which are protected by certain symmetries. Most of the Dirac semimetals discussed in literature are non-magnetic. In this talk, I will illustrate that Dirac semimetals can also exist in magnetic systems whose symmetry are described by magnetic space groups. The degeneracy at the Dirac point can be protected by four-dimensional irreducible projective representations (Reps) of the little co-group at high symmetry points at the boundary of the Brillouin zone. To search for the Dirac cones, we develop a systematic method to obtain all the irreducible projective Reps of magnetic point groups, and further provide a method to judge if the dispersion around the degeneracy point is linear or not. From above information, one can tell which magnetic space group can protect magnetic Dirac semimetals at their high symmetry points. Our results are helpful for experimental realization of such magnetic Dirac semimetals.