Enhanced indirect exchange interactions in the presence of circular potentials in graphene

We calculate indirect exchange interaction between two magnetic impurities in pristine graphene in the presence of a circular potential. In bulk graphene structures indirect exchange interaction, also known as RKKY (Ruderman-Kittel-Kasuya-Yosida) interaction, shows a power-law decay with distance for both doped and undoped cases. Here we show that under a circular electric potential quasibound states lead to enhanced RKKY interactions between magnetic moments located in the vicinity of the potential well. It is shown that the strength of the potential well and Fermi energy can be tuned to create enhanced, nondecaying, long ranged RKKY interactions. We show that when the Fermi level lies at the quasibound state energy, the scattering processes between the states of the same chirality dominate over the other scattering channels and this leads to a predominantly ferromagnetic, nondecaying interaction between the impurities at long distances. The predicted effect can enable electrical control of RKKY interactions in graphene or other two-dimensional materials.