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 behavior 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 tight-binding models in real space. Based on this finding, we show how using a lead far away from the spins can switch the coupling on and off among them nonlocally.

• Received 3 June 2018
• Revised 15 August 2018

DOI:https://doi.org/10.1103/PhysRevB.99.121409