RKKY interaction in helical higher-order topological insulators

TL;DR

This paper provides a theoretical analysis of RKKY interactions in helical higher-order topological insulators, revealing distinct behaviors mediated by hinge and bulk carriers, with implications for quantum device design.

Contribution

It introduces a detailed theoretical model of RKKY interactions in HOTIs, highlighting the different mediating mechanisms and their unique decay and oscillation characteristics.

Findings

Hinge-mediated interactions include Heisenberg, Ising, and DM terms with specific decay and oscillation patterns.

Bulk-mediated interactions involve Heisenberg, twisted Ising, and DM terms with cubic decay.

Distinct behaviors of RKKY interactions in hinge and bulk regions influence HOTI properties.

Abstract

We theoretically investigate the RKKY interaction in helical higher-order topological insulators (HOTIs), revealing distinct behaviors mediated by hinge and Dirac-type bulk carriers. Our findings show that hinge-mediated interactions consist of Heisenberg, Ising, and Dzyaloshinskii-Moriya (DM) terms, exhibiting a decay with impurity spacing z and oscillations with Fermi energy {\epsilon}F . These interactions demonstrate ferromagnetic behaviors for the Heisenberg and Ising terms and alternating behavior for the DM term. In contrast, bulk-mediated interactions include Heisenberg, twisted Ising, and DM terms, with a conventional cubic oscillating decay. This study highlights the nuanced interplay between hinge and bulk RKKY interactions in HOTIs, offering insights into the design of next-generation quantum devices based on the HOTIs.