Topological Superconductivity and High Chern Numbers in 2D Ferromagnetic Shiba Lattices

Inspired by the recent experimental observation of topological superconductivity in ferromagnetic chains, we consider a dilute 2D lattice of magnetic atoms deposited on top of a superconducting surface with a Rashba spin-orbit coupling. We show that the studied system supports a generalization of p(x) + ip(y) superconductivity and that its topological phase diagram contains Chern numbers higher than xi/a(>> 1), where xi is the superconducting coherence length and a is the distance between the magnetic atoms. The signatures of nontrivial topology can be observed by STM spectroscopy in finite-size islands.