Screening of Coulomb interaction and π magnetism in defected graphene

Abstract

Recent scanning tunneling microscopy experiments have revealed the itinerant character of $\ensuremath{\pi}$ magnetism in defected graphene. Employing the constrained random-phase approximation, I calculate the strength of the effective screened Coulomb interaction (Hubbard $U$) for bare and hydrogen-passivated vacancies in graphene. I find that vacancy defects lead to a reduction in screened Coulomb interactions compared to graphene. Screening strongly depends on the concentration of vacancies, passivation, and the position of vacancies in the graphene lattice. For hydrogen-passivated vacancies ${p}_{z}$ orbitals are very well screened, suggesting a strong itinerant character of $\ensuremath{\pi}$ magnetism. On the basis of local $U$ parameters, I discuss the instability of the paramagnetic state of the defected graphene towards the ferromagnetic within the Stoner model. $\ensuremath{\pi}$ magnetism survives at high concentrations of vacancies when the ordered vacancies belong to the same sublattices. For completeness, the long-range Coulomb interactions for both passivated and unpassivated vacancies are also reported. For vacancies in the same sublattices, the interactions turn out to be local, and the nonlocal part is strongly screened due to $\ensuremath{\pi}$ states, making defected graphene a correlated system.