Based on their formation mechanisms, Dirac points in three-dimensional systems can be classified as accidental or essential. The former can be further distinguished into type-I and type-II, depending on whether the Dirac cone spectrum is completely tipped over along certain direction. Here, we predict the coexistence of all three kinds of Dirac points in the low-energy band structure of CaAgBi-family materials with a stuffed Wurtzite structure. Two pairs of accidental Dirac points reside on the rotational axis, with one pair being type-I and the other pair type-II; while another essential Dirac point is pinned at the high symmetry point on the Brillouin zone boundary. Due to broken inversion symmetry, the band degeneracy around accidental Dirac points is completely lifted except along the rotational axis, which may enable the splitting of chiral carriers at a ballistic p-n junction with a double negative refraction effect. We clarify their symmetry protections, and find both the Dirac-cone and Fermi arc topological surface states.
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