Topological properties of superconductive transition metal phosphorus compounds

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Based on the first-principles calculations and effective k⋅p model, we propose the topological nodal-line (NL) semimetal state in the family of non-centro-symmetric ternary transition metal phosphorus compounds TRuX (T=Zr, Hf, Nb; X = P, As), when the spin-orbit coupling (SOC) is ignored. A K-point centered nodal line on the kz = 0 plane is protected by the mirror symmetry Mz. When SOC is considered, the gap opens along the NL in the kz=0 plane. But, at the kz = ±0.015*2πc planes, there are 12 pairs of Weyl points. The Berry phase, Berry curvature and Fermi Arc of those Weyl points are found. In these compounds, the Fu-Kane Z2 invariant is trivial (0;000), but the mirror Chern number is 2. Since these compounds show superconductivity at about 11 K, they might be mirror symmetry protected topological superconductors.