Topological Yu-Shiba-Rusinov chain from spin-orbit coupling

We investigate the possibility of realizing a topological state in the impurity band formed by a chain of classical spins embedded in a two-dimensional singlet superconductor with Rashba spin-orbit coupling. In contrast to similar proposals which require a helical spin texture of the impurity spins for a nontrivial topology, here we show that spin-flip correlations due to the spin-orbit coupling in the superconductor produces a topological state for ferromagnetic alignment of the impurity spins. From the Bogoliubov--de Gennes equations we derive an effective tight-binding model for the subgap states which resembles a spinless superconductor with long-range hopping and pairing terms. We evaluate the topological invariant, and show that a topologically nontrivial state is generically present in this model.