In this paper, we propose $\mathrm{ CeCoIn_5}/\mathrm{ YbCoIn_5}$ superlattice systems as a test bed for the reduction of topological classification in free fermions. We find that the system with quad-layer of $\mathrm{ CeCoIn_5}$ shows a topological crystalline superconducting phase with the mirror Chern number eight at the non-interacting level. Furthermore, we demonstrate that in the presence of two-body interactions, gapless edge modes are no longer protected by the symmetry in the system with quad-layer, but are protected in the systems with bi- or tri-layer. This clearly exemplifies the reduction of topological classification from $\mathbb{ Z}\oplus\mathbb{ Z}$ to $\mathbb{ Z}\oplus\mathbb{ Z}_8$.
Categories: cond-mat.str-el