RKKY interaction in bilayer graphene

• We study the RKKY interaction in bilayer graphene (BLG) in the four-band model.
• Long-distance behavior of RKKY in BLG is unlike that in other 2D electron gases.
• RKKY interaction in BLG is considered in both weak and strong interlayer coupling.

We study the RKKY interaction between two magnetic impurities located on the same layer (intralayer case) or on different layers (interlayer case) in undoped bilayer graphene (BLG) in the four-bands model, by directly calculating the Green functions in the eigenvalues and eigenvectors representation. Our results show that both intra- and interlayer RKKY interactions between two magnetic impurities located on the same (opposite) sublattice are always ferromagnetic (antiferromagnetic). Furthermore we find unusual long-distance decay of the RKKY interaction in BLG. The intralyer RKKY interactions between two magnetic impurities located on the same sublattice, JAnAn(R)JAnAn(R) and JBnBn(R)JBnBn(R), decay closely as 1/R61/R6 and 1/R21/R2 at large impurity distances respectively, but when they are located on opposite sublattices the RKKY interactions exhibit 1/R41/R4 decays approximately. In the interlayer case, the RKKY interactions between two magnetic impurities located on the same sublattice show a decay close to 1/R41/R4 at large impurity distances, but if two magnetic impurities be on opposite sublattices the RKKY interactions, JA1B2(R)JA1B2(R) and JB1A2(R)JB1A2(R), decay closely as 1/R61/R6 and 1/R21/R2 respectively. Both intra- and interlayer RKKY interactions have anisotropic oscillatory factors which for intralayer case is equal to that for single layer graphene (SLG). Our results at weak and strong interlayer coupling limits reduce to the RKKY interaction of SLG and that of BLG in the two-bands approximation respectively.