RKKY interaction at helical edges of topological superconductors

TL;DR

This paper investigates how magnetic impurities interact at the edges of topological superconductors, revealing edge-aligned spins and a Majorana-mediated ferromagnetic RKKY interaction, which could serve as a detection method for Majorana states.

Contribution

It provides a combined analytical and numerical analysis of impurity spin configurations and RKKY interactions at topological superconductor edges, highlighting the role of Majorana edge states.

Findings

Single impurity spins align along the edge due to anisotropy.

RKKY interaction is mainly mediated by Majorana edge states.

Impurities tend to ferromagnetically align along the edge.

Abstract

We study spin configurations of classical magnetic impurities placed close to the edge of a two-dimensional topological superconductor both analytically and numerically. First, we demonstrate that the spin of a single magnetic impurity close to the edge of a topological superconductor tends to align along the edge. The strong easy-axis spin anisotropy behind this effect originates from the interaction between the impurity and the gapless helical Majorana edge states. We then compute the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between two magnetic impurities placed close to the edge. We show that, in the limit of large interimpurity distances, the RKKY interaction between the two impurities is mainly mediated by the Majorana edge states and leads to a ferromagnetic alignment of both spins along the edge. This effect could be used to detect helical Majorana edge states.