INDIRECT EXCHANGE INTERACTIONS IN GRAPHENE

We study the Ruderman-Kittel-Katsuya-Yoshida (RKKY) interactions in graphene controlling the gate voltage and applying nonmagnetic disorder. It is found that oscillations of the RKKY interactions in undoped graphene are characterized by the interference of two neighbor Dirac nodes K and K' in the first Brillouin zone and decays with R-3 distance dependence. In the slightly doped graphene, a beating pattern, which consists of two characteristic wavevectors (K-K and k(F)), starts to appear. The distance dependence in this regime shows a crossover from the R-3 to R-2. We present the effect of weak disorder on the RKKY interactions in diffusive regime. The arithmetic averaged interaction over disorder configurations decreases exponentially at distances exceeding the elastic mean free path, while the geometrical average(typical) value has the same power-law as the clean limit.