Fate of Majorana modes in $\mathrm{CeCoIn}_5$/$\mathrm{YbCoIn}_5$ superlattices -a test bed for reduction of topological classification-

Abstract

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 $\mathbb{Z}\oplus\mathbb{Z}_8$.