Topological superconductivity and high Chern numbers in ferromagnetic Shiba lattices

Topological superconductivity was recently observed in a system consisting of a 1D magnetic adatoms on top of a superconducting surface. Anticipating further developments, we show that a 2D array of magnetic atoms support a variant of $p_x+ip_y$ superconductivity and exhibit very complex phase diagram with high Chern numbers. We also present a detailed study of Majorana bound states in 1D chains.