Non-exponential long-range interaction of magnetic impurities in spin-orbit coupled superconductors

TL;DR

This paper reveals a novel 1/r^2 long-range interaction between magnetic impurities in 2D spin-orbit coupled superconductors, mediated by the Goldstone mode, challenging the conventional exponential decay expectation.

Contribution

It demonstrates that spin-orbit coupling induces a long-range interaction via the Goldstone mode, which persists beyond the superconductor's coherence length in 2D systems.

Findings

Long-range 1/r^2 interaction mediated by Goldstone mode.

Interaction persists beyond the coherence length.

Potential impact on spin order and Majorana fermions.

Abstract

The Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction of magnetic impurities in a superconductor exponentially decreases when the distance $r$ between them is larger than the superconductor's coherence length, because this interaction is mediated by quasiparticles which have a gap in their energy spectrum. At the same time, the spin-singlet superconducting condensate was always assumed to stay neutral to magnetic impurities. Due to a spin-orbit coupling (SOC), however, Cooper pairs gain an admixture of spin-triplet correlated states which provide for a link between impurity spins and an s-wave condensate. It is shown that its static Goldstone mode mediates the $1/r^2$ interaction of the spins in two-dimensional (2D) systems. This effect is considered within two models: of a clean 2D s-wave superconductor with the strong Rashba SOC and of a bilayer system combining a 2D Rashba coupled electron gas and an s-wave superconducting film. The predicted long-range interaction can have a strong effect on a spin order in superconductor-magnetic impurity systems that are expected to host Majorana fermions.