Noncentrosymmetric Line-Node Dirac semimetal CaAgX (X=P, As)

Noncentrosymmetric ternary pnictide CaAg$X$ ($X=$P, As) is shown to be a topological line-node semimetal protected solely by mirror-reflection symmetry. The band gap vanishes on a circle in momentum space and surface states emerge within the circle. The $Z_2$ topological invariant $\nu$ related to the surface states is defined from the Berry phase and mirror-reflection symmetry. Extending this study to spin-orbit coupled systems reveals that, compared with CaAgP, a substantial band gap is induced in CaAgAs by large spin-orbit interaction. The resulting states are a topological insulator, in which the $Z_2$ topological invariant is given by 1;000. We have found that the $Z_2$ topological invariants $\nu_0$, $\nu_1$, $\nu_2$, and $\nu_3$ for time-reversal-invariant insulators without spatial-inversion symmetry and with mirror-reflection symmetry are calculated from the $Z_2$ invariant $\nu$ for a line node in the absence of spin-orbit interaction. Namely, line-node Dirac semimetals protected by mirror-reflection symmetry turn into strong topological insulators owing to spin-orbit interaction. [AY, Y. Yamakawa, Y. Tanaka, and Y. Okamoto, arXiv:1510.00202]