Spin-1 Dirac-Weyl fermions protected by bipartite symmetry.

We propose that bipartite symmetry allows spin-1 Dirac-Weyl points, a generalization of the spin-1/2 Dirac points in graphene, to appear as topologically protected at the Fermi level. In this spirit, we provide methodology to construct spin-1 Dirac-Weyl points of this kind in a given 2D space group and get the classification of the known spin-1 systems in the literature. We also apply the workflow to predict two new systems, P3m1-9 and P31m-15, to possess spin-1 at K/K' in the Brillouin zone of hexagonal lattice. Their stability under various strains is investigated and compared with that of T3, an extensively studied model of ultracold atoms trapped in optical lattice with spin-1 also at K/K'.