Electronic and magnetic properties of graphene quantum dots with two charged vacancies

Electronic and magnetic properties of a system of two charged vacancies in hexagonal shaped graphene quantum dots are investigated using a mean-field Hubbard model as a function of the Coulomb potential strength $\beta$ of the charge impurities and the distance R between them. For $\beta=0$, the magnetic properties of the vacancies are dictated by Lieb's rules where the opposite (same) sub-lattice vacancies are coupled antiferromagnetically (ferromagnetically) and exhibit Fermi oscillations. Here, we demonstrate the emergence of a non-magnetic regime within the subcritical region: as the Coulomb potential strength is increased to $\beta \sim 0.1$ , before reaching the frustrated atomic collapse regime, the magnetization is strongly suppressed and the ground state total spin is given by $S_{z}=0$ both for opposite and same sublattice vacancy configurations. When long-range electron-electronz in-teractions are included within extended mean-field Hubbard model, the critical value for the frustrated collapse increases from $\beta_{cf} \sim 0.28$ to $\beta_{cf} \sim 0.36$ for $R < 27 \ \r{A}$ .