By using first-principles calculations and a $k·p$ model analysis, we propose that the three-dimensional topological nodal line semimetal state can be realized in the ${\mathrm{CaP}}_3$ family of materials, which includes ${\mathrm{CaP}}_3,{\mathrm{CaAs}}_3,{\mathrm{SrP}}_3,{\mathrm{SrAs}}_3$, and ${\mathrm{BaAs}}_3$, when spin-orbit coupling (SOC) is ignored. The closed topological nodal line near the Fermi energy is protected by time reversal symmetry and spatial inversion symmetry. Moreover, drumheadlike two-dimensional surface states are also obtained on the $c$-direction surface of these materials. When SOC is included, the gaps open along the nodal line and these materials become strong topological insulators with $Z_2$ indices as $(1;010)$.

• Received 13 September 2016
• Revised 9 December 2016

DOI:https://doi.org/10.1103/PhysRevB.95.045136