Mapping rules from nodal line semimetal to topological crystalline insulator in face centered cubic lattice

We study what kind of topological crystalline insulator phase emerges from nodal line semimetal phases in the face centered cubic system, which is not indicated by topological indices when spin-orbit coupling (SOC) is introduced. We construct an effective model, which hosts two different nodal lines phases, and calculated mirror Chern numbers in it by introducing SOC. As a result, we find that the two nodal line phases with different nodal line configurations are mapped to different topological crystalline insulator phases. This result shows that turning off SOC and checking the nodal line configuration can distinguish the two topological crystalline insulator phases, which have not been distinguished by previous methods.