In this work we consider the influence of potential impurities deposited on top of two-dimensional chiral superconductors. As discovered recently, magnetic impurity lattices on an $s$-wave superconductor may give rise to a rich topological phase diagram. We show that a similar mechanism takes place in chiral superconductors decorated by nonmagnetic impurities, thus avoiding the delicate issue of magnetic ordering of adatoms. We illustrate the method by presenting the theory of potential impurity lattices embedded on chiral $p$-wave superconductors. While a prerequisite for the topological state engineering is a chiral superconductor, the proposed procedure results in vistas of nontrivial descendant phases with different Chern numbers.

• Received 28 April 2016

DOI:https://doi.org/10.1103/PhysRevB.94.060505