Fragile boundary modes and corner states in spin-polarized Yu-Shiba-Rusinov networks without spin-orbit interactions

Topological superconductors support extended boundary modes robust to static disorder which makes them attractive materials for topological quantum computing. Typically, spin-orbit interactions are necessary for a system to undergo a topological phase transition. In this talk, we will present theoretical calculations of weak topological superconductivity with fragile edge modes and corner states without any spin-orbit coupling in a spin-polarized Yu-Shiba-Rusinov (YSR) network. We construct a YSR network by decorating a conventional two-dimensional superconducting network with magnetic impurities. We identify bulk-separated fragile boundary modes in topologically trivial superconducting phases arising from weakly coupled YSR states in the network, and we show how they are distinguished from topological boundary modes that are connected to the bulk via the spectral flow principle. We then discuss how a similar YSR superlattice without the network geometry fails to generate a topological phase, indicating the network geometry plays a crucial role in the realization of boundary modes. Our work demonstrates a novel approach to topological superconductivity using superconducting networks and identifies the possibility of topologically trivial boundary modes in other Shiba superlattices.