RKKY Interaction On Surfaces of Topological Insulators With Superconducting Proximity Effect

TL;DR

This paper studies how superconductivity affects the magnetic interactions between impurities on topological insulator surfaces, revealing a long-range antiferromagnetic RKKY interaction influenced by spin-orbit coupling and superconducting coherence.

Contribution

It provides a detailed analysis of the RKKY interaction in topological insulators with superconducting proximity, highlighting the long-range behavior and conditions for Yu-Shiba-Rusinov states.

Findings

Superconductivity induces a long-range in-plane antiferromagnetic RKKY interaction.

The interaction decays as 1/r for distances less than the coherence length.

Conditions for Yu-Shiba-Rusinov intragap states are identified.

Abstract

We consider the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between magnetic impurities on the surface of a three-dimensional topological insulator with proximity induced superconductivity. A superconductor placed on the top of the topological insulator induces a gap in the surface electron states and gives rise to a long-ranged in-plane antiferromagnetic RKKY interaction. This interaction is frustrated due to strong spin-orbit coupling, decays as $1/r$ for $r<\xi$, where $r$ is the distance between two magnetic impurities and $\xi$ the superconducting coherence length, and dominates over the ferromagnetic and Dzyaloshinskii-Moriya type interactions for $r>\xi$. We find the condition for the Yu-Shiba-Rusinov intragap states that are bound to the magnetic impurities.