The mechanisms of impurity–impurity and impurity–matrix interactions in B/N-doped graphene

Using DFT calculations, we investigate mechanisms of the impurity–impurity and impurity–matrix interactions in B/N-doped graphene. Our results have revealed that the impurities interact with each other through the long-range screened Coulomb interaction, and the impurity–matrix interaction is understood from the orbital hybridization. The impurity-induced inter-valley interference only shows a minor modification on the Coulombic impurity–impurity interaction. The B impurity binds more strongly with the matrix than the N impurity. The variation of the Fermi-level energy relative to Dirac point with the itinerant carrier concentration, along with the delocalized distribution of the carriers, indicates the nonlocal doping effect of the impurities.