Indirect exchange interaction between magnetic impurities near the helical edge

TL;DR

This paper investigates the indirect exchange interaction between magnetic impurities in a 2D topological insulator, revealing a novel interference effect between bulk and edge states that influences magnetic coupling.

Contribution

It introduces a new understanding of how bulk-edge interference affects magnetic interactions, highlighting a dominant contribution near the edge with oscillatory behavior.

Findings

Interference between bulk and edge states creates a unique exchange interaction component.

This interference term decays exponentially and oscillates with distance.

The effect is significant when one impurity is near the edge and the other in the bulk.

Abstract

The indirect exchange interaction between magnetic impurities located in the bulk of a two-dimensional topological insulator decays exponentially with the distance. The indirect exchange interaction for magnetic impurities mediated by the helical states at the edge of the topological insulator demonstrates behaviour which is typical for the Ruderman-Kittel-Kasuya-Yosida interaction in a one-dimensional metal. We have shown that interference between the bulk and edge states in the two-dimensional topological insulator results in existence of the unusual contribution to the indirect exchange interaction which, on the one hand, decays exponentially with a distance at the length scale controlled by the Fermi energy of the edge states and, on the other hand, oscillates with distance along the helical edge with the period determined by the Fermi wave length. We found that this interference contribution to the indirect exchange interaction becomes dominant for such configurations of two magnetic impurities when one of them is situated close to the helical edge whereas the other one is located far away in the bulk.