Interaction between K adatoms on graphene is investigated by first-principles calculations based on density function theory and analytical analyses based on the k• p perturbation theory. The calculation shows that there is a strong repulsion between K adatoms. The main origin of this strong repulsion is not from the dipole-dipole interaction as suggested for K adatom on graphite surface, but comes from the screened Coulomb interaction. Potassium adatom on graphene donates its s electron and becomes K + . The positively charged K adatom induces electron density oscillation on graphene which is responsible for the screened Coulomb repulsion between the K adatoms.PACS numbers: 68.65. Pq, 68.43.Fg, 71.15.Mb, 68.55.Ln § xiaojie@csrc.ac.cn * wangcz@ameslab.gov # kchang@semi.ac.cn 1 Coulomb impurity in graphene is a problem of fundamental interest due to the unique electronic structure of graphene. Because graphene has linear energy dispersion and very small density-of-states around the Fermi level and consists of two sub-lattices, the electronic structure and transport properties of graphene are very sensitive to impurities [1][2][3][4][5][6][7][8]. Understanding and manipulating the interaction among the Coulomb impurities and between the impurity atoms and carbon atoms on graphene provide an effective approach for engineering the electronic structures to meet various requirements in the application of graphene.While it is well-known that Coulomb or magnetic impurities on metal surface induce interesting phenomena such as Friedel oscillation in electron density thus the indirect interaction between the impurities, interaction between such impurities on graphene has not been well understood. It has been proposed that oscillation of the charge density induced by a charged impurity on graphene has a faster (δρ ~ r -3 ) decay than that in conventional 2D electron systems which decay as r -2 [5,7]. Calculations based on tight-binding models suggested that in addition to the long wavelength Friedel oscillation, a short wavelength modulation of electron density also emerges due to the two sub-lattices on graphene [4,9]. Energy-resolved maps of the local density-of-states by using STM also reveal electron density modulations on two different length scales, reflecting both intravalley and intervalley scattering [8].Despite of intensive studies, our understanding of the behavior of charge oscillation and especially impurity interactions on graphene is still far from being completed.Most of the previous theoretical studies are based on model Hamiltonians, a fully self-consistent first-principles calculation is highly desirable and can provide useful insight for a better understanding of the mechanism of impurities on graphene.In this paper, we performed first-principles calculations and analytical analyses based on the k•p perturbation theory to study the interaction between K adatoms on graphene and characterize the electron density oscillation behavior induced by the K adatoms. Potassium on graphene is chosen because ...