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Phosphorene is an anisotropic puckered two-dimensional ($2$D) hexagonallattice of phosphorus atoms. The edge modes in a zigzag phosphorene nanoribbon(ZPNR) are quasi-flat in nature and fully isolated from the bulk states, whichare unique in comparison to the other hexagonal lattices like graphene,silicene etc. We theoretically investigate the Ruderman-Kittel-Kasuya-Yosida(RKKY) exchange interaction between two magnetic impurities placed on thenanoribbon, and extract the signatures of the flat edge states via the behaviorof it. Due to the complete separation of the edge states from the bulk, we canisolate the edge mode contribution via the RKKY interaction from that of thebulk by tuning the external gate potential when both the impurities are placedat the same edge. The bulk induced RKKY interaction exhibits very smoothoscillation with the distance between the two impurities, whereas for edgemodes it fluctuates very rapidly. We also explore the effect of tensile strainboth in absence and presence of gate voltage and reveal that the RKKYinteraction strength can be boosted under suitable doping, when both theimpurities are within the bulk.

Probing the edge states in a zigzag phosphorene nanoribbon via RKKY exchange interaction