Long-range and tunable RKKY interaction in the topological channel of gated bilayer graphene

Two separate gate electrodes with opposite gate voltages can drive an AB-stacked bilayer graphene (BLG) under them into different quantum valley Hall states. And between the two topological domains there appears a one-dimensional boundary, dubbed the topological channel (TC). By means of the Lanczos method, we theoretically study the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between two magnetic impurities in such a TC of BLG. We find that the RKKY interaction is long-range with an ${R}^{\ensuremath{-}1}$ decay rate as the distance $R$ between two magnetic impurities increases, whereas the slowest decay rate in any graphene structure is ${R}^{\ensuremath{-}2}$ according to previous literature. Moreover, we also find that the strength and sign of the RKKY interaction in the TC can be readily controlled by altering the gate voltage or carrier doping. Such a tunable and ${R}^{\ensuremath{-}1}$ decaying RKKY interaction implies the possibility of establishing and controlling a long-range magnetic ordering state in a dilute magnetic impurity-doped BLG.