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.

Figure 1

Topological phase diagram for the effective model as a function of $k_{F}a$ and $\tilde{\lambda }$. The topological regions are shaded according to the magnitude of the gap, while the nontopological regions are left blank. Red lines indicate the boundary between topological and nontopological phases. We have chosen ${\epsilon }_0=0$ for the isolated impurity level and ${\xi }_0=5a$ for the superconducting coherence length at $\tilde{\lambda }=0$, which ensures that the impurity band remains within the superconducting gap. The impurity spins point in the $x\text{−}z$ plane. The large values of $k_{F}a$ allow us to utilize the asymptotic expressions for the entries in Eq. (19).