Non-local control of spin-spin correlation in finite geometry helical edge

TL;DR

This paper investigates how finite geometry in quantum Hall and spin-Hall systems enables non-local spin-spin interactions through the system's perimeter, challenging previous assumptions about edge behavior.

Contribution

It reveals the breakdown of traditional edge interaction restrictions in finite systems and proposes a method to control spin coupling non-locally using distant leads.

Findings

Long-range spin interactions occur via the perimeter in finite systems.

A lead far from spins can switch their coupling on and off.

Analytical and tight-binding models confirm the non-local control mechanism.

Abstract

An infinite edge of a quantum Hall system prohibits indirect exchange coupling between two spins whereas a quantum spin-Hall edge prohibits out-of-plane coupling. In this study we analyze an unexpected breakdown of this behaviors in a finite system, where the two spins can interact also via a longer path that traverses the whole perimeter of the system. We explain this using an analytical model as well as using tight binding models in real space. Based on this finding, we propose how using a lead far away from the spins can switch the coupling on and off among them non-locally.