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In this work we will explore the properties of superconducting surfacesdecorated by two-dimensional ferromagnetic adatom lattices. As discoveredrecently [R\"ontynen and Ojanen, Phys. Rev. Lett. \textbf{114}, 236803 (2015)],in the presence of a Rashba spin-orbit coupling these systems may supporttopological superconductivity with complex phase diagrams and high Chernnumbers. We show how the long-range hopping nature of the effective low-energytheory generically gives rise to a phase diagram covered by a \emph{Chernmosaic} -- a rich pattern of topological phases with large Chern numbers. Westudy different lattice geometries and the dependence of energy gaps andabundance of different phases as a function of system parameters. Our findingsestablish the studied system as one of the richest platforms for topologicalmatter known to date.

Chern mosaic - topology of chiral superconductivity on ferromagnetic adatom lattices