Chern mosaic: Topology of chiral superconductivity on ferromagnetic adatom lattices

In this work, we will explore the properties of superconducting surfaces decorated by two-dimensional ferromagnetic adatom lattices. As discovered recently [Röntynen and Ojanen, Phys. Rev. Lett. 114, 236803 (2015)PRLTAO0031-900710.1103/PhysRevLett.114.236803], in the presence of a Rashba spin-orbit coupling these systems may support topological superconductivity with complex phase diagrams and high Chern numbers. We show how the long-range hopping nature of the effective low-energy theory generically gives rise to a phase diagram covered by a Chern mosaic, a rich pattern of topological phases with large Chern numbers. We study different lattice geometries and the dependence of energy gaps and abundance of different phases as a function of system parameters. Our findings establish the studied system as one of the richest platforms for topological matter known to date.