RKKY interaction in helical higher-order topological insulators

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 $\varepsilon_F$. 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.