Controlling the RKKY interaction and heat transport in a Kitaev spin liquid via $Z_2$ flux walls

Kitaev spin liquids (KSLs) contain both itinerant Majorana fermions and localized $Z_2$ flux excitations. The mobile fermions transport energy, while the fluxes hinder heat flow. By controlling the flux configuration, one can separate a KSL into different domains via $Z_2$ flux walls. We show that at low temperatures, the wall significantly suppresses the Majorana-mediated Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction and blocks the heat transfer between domains.