Topological semimetals with triply degenerate nodal points in θ -phase tantalum nitride

Using first-principles calculation and symmetry analysis, we propose that θ-TaN is a topological semimetal having a new type of point nodes, i.e., triply degenerate nodal points. Each node is a band crossing between degenerate and nondegenerate bands along the high-symmetry line in the Brillouin zone, and is protected by crystalline symmetries. Such new type of nodes will always generate singular touching points between different Fermi surfaces and three-dimensional spin texture around them. Breaking the crystalline symmetry by external magnetic field or strain leads to various topological phases. By studying the Landau levels under a small field along the c axis, we demonstrate that the system has a new quantum anomaly that we call ``helical anomaly.'