RKKY interaction in graphene bubbles

By means of the Lanczos method, a numerically efficient theoretical approach, we study the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction in a graphene bubble. We find that the RKKY interaction in a graphene bubble can be larger or smaller than the corresponding result in pristine graphene by a few orders of magnitude, depending on the sublattice attribution and pseudomagnetic field strength where two magnetic impurities are positioned, which is due to the sublattice polarization of the low-energy electronic states in a strong pseudomagnetic field. If two magnetic impurities are both in the bubble region, the ${R}^{\ensuremath{-}3}$ decay rate of the RKKY interaction found in pristine graphene breaks down. But it recovers when one magnetic impurity is far away from the bubble center no matter where another impurity is located. When the Fermi level deviates from the Dirac point by carrier doping, the antiferromagnetic RKKY interaction between two magnetic impurities located at the opposite sublattices can be inverted to be ferromagnetic by altering the bubble height properly.