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

TL;DR

This paper demonstrates that a chain of classical spins in a 2D superconductor with Rashba spin-orbit coupling can host a topological state without requiring helical spin textures, due to spin-flip correlations.

Contribution

It introduces a new mechanism for topological states in impurity chains, relying on spin-orbit coupling-induced correlations rather than helical spin arrangements.

Findings

Topological states are achievable with ferromagnetic impurity chains.

Derived an effective tight-binding model resembling a spinless superconductor.

Topological invariant analysis confirms the presence of non-trivial states.

Abstract

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 non-trivial state is generically present in this model.